10th Class Mathematics Introduction to Trigonometry Question Bank

done Assertion And Reason (MCQs) - Introduction to Trigonometry Total Questions - 14

• question_answer1)

  Directions (Q. Nos. 1 - 14): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:

  Assertion (A): The value of each of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangle, if the angle remains the same.

  Reason (R): In right \[\Delta ABC,\] \[\angle B=90{}^\circ \] and \[\angle A=\theta ,\]\[\sin \theta =\frac{BC}{AC}<1\]and \[\cos \theta =\frac{AB}{AC}<1\]as hypotenuse is the longest side.

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer2)

  Assertion (A): In \[\Delta ABC,\] right angled at B, if \[\sin A=\frac{8}{17},\]then \[\cos A=\frac{15}{17}\]and \[\tan A=\frac{8}{15}\].

  Reason (R): For acute angle \[\theta ,\] \[\cos \theta =\frac{Hypotenuse}{Base},\]and \[\tan \theta =\frac{Base}{Perpendicular}\].

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer3)

  Assertion (A): In \[\Delta PQR\] right angled at Q, \[\text{QR}=\text{3 cm}\] and \[\text{PR}-\text{PQ}=\text{1 cm}\]. The value of \[{{\sin }^{2}}R+\text{cosec}\,\text{R}\]is \[\frac{189}{100}\].

  Reason (R): \[{{\sin }^{2}}A={{(\sin A)}^{2}}\]  and \[\text{cosec A}={{(\sec A)}^{-1}}\] .

   
  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer4)

  Assertion (A): ABCD is a rectangle such that \[\angle CAB=60{}^\circ \]and \[\text{AC}=\text{a}\] units. The area of rectangle ABCD is \[\frac{\sqrt{3}}{2}{{a}^{2}}\].

  Reason (R): The value of \[\sin 60{}^\circ \] is \[\frac{\sqrt{3}}{2}\] and \[\cos 60{}^\circ \]is \[\frac{1}{2}\].

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer5)

  Assertion (A): If \[\sin \theta =\frac{1}{2}\] and \[\theta \] is acute angle, then \[(3\cos \theta -4{{\cos }^{3}}\theta )\]is equal to 0.

  Reason (R): As \[\sin \theta =\frac{1}{2}\] and \[\theta \] is acute, so \[\theta \] must be \[60{}^\circ \].

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false  done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer6)

  Assertion (A): x\[{{\cos }^{2}}A-{{\sin }^{2}}A=1,\] \[{{\tan }^{2}}A-{{\sec }^{2}}A=1\] are trigonometric identities.

  Reason (R): An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angles involved.

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer7)
  Assertion (A): If \[\sec \theta +\tan \theta =x,\] then the value of \[\sin \theta =\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\]. Reason (R): If \[\sec \theta +\tan \theta =x,\]then \[x+\frac{1}{x}=2\tan \theta \] and \[x-\frac{1}{x}=2\sec \theta \].
  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer8)

  Assertion (A): \[({{\cos }^{2}}\theta -{{\sin }^{2}}\theta )=\frac{2\tan \theta }{(1-{{\tan }^{2}}\theta )}\] is not an identity.        ;

  Reason (R): A equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of angles involved.

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer9)

  Assertion (A): \[\frac{\sin \theta -2{{\sin }^{3}}\theta }{2{{\cos }^{3}}\theta -\cos \theta }=\tan \theta ,\] where \[\theta \] is acute angle.

  Reason (R): For acute angle A, \[\tan A=\frac{\sin A}{\cos A}\]and \[{{\sin }^{2}}A+{{\cos }^{2}}A=1.\]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer10)

  Assertion (A): The value of \[\sin \theta =\frac{4}{3}\] in not possible.

  Reason (R): Hypotenuse is the Largest side in any right angled triangle.

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer11)

  Assertion (A): \[{{\sin }^{2}}67{}^\circ +{{\cos }^{2}}67{}^\circ =1\]

  Reason (R): For any value of \[\theta ,\] \[{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1\]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer12)

  Assertion (A): In a right angled triangle, if \[\tan \theta =\frac{3}{4},\] the greatest side of the triangle is 5 units.

  Reason (R): \[{{\text{(greatest side})}^{2}}=\]\[{{(\text{hypotenuse})}^{\text{2}}}={{(\text{perpendicular})}^{\text{2}}}+{{(\text{base})}^{2}}\]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)   done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer13)

  Assertion (A): lf \[\cos A+{{\cos }^{2}}A=1\]then \[{{\sin }^{2}}A+{{\sin }^{4}}A=2.\]

  Reason (R): \[1-{{\sin }^{2}}A={{\cos }^{2}}A,\] for any value of A.

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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• question_answer14)

  Assertion (A): In a right angled triangle, if \[\cos \theta =\frac{1}{2}\] and \[\sin \theta =\frac{\sqrt{3}}{2},\] then \[\tan \theta =\sqrt{3}\].

  Reason (R): \[\tan \theta =\frac{\sin \theta }{\cos \theta }\]

  A)
  Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) done clear
  B)
  Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A) done clear
  C)
  Assertion (A) is true but Reason (R) is false done clear
  D)
  Assertion (A) is false but Reason (R) is true done clear
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