10th Class Mathematics Introduction to Trigonometry Question Bank MCQs - Introduction to Trigonometry

  • question_answer
    If \[\cos A=\frac{4}{5},\]then the value of \[\tan A\] is:                                                       (NCERT EXEMPLAR)

    A) \[\frac{3}{5}\]

    B) \[\frac{3}{4}\]

    C) \[\frac{4}{3}\]

    D) \[\frac{5}{3}\]

    Correct Answer: B

    Solution :

    [b] Given, \[\cos A=4/5\]
    \[\sin A=\sqrt{1-{{\cos }^{2}}A}\]\[[{{\sin }^{2}}A+{{\cos }^{2}}A=1]\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\sin A=\sqrt{1-{{\left( \frac{4}{5} \right)}^{2}}}=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}\]
    Now,  \[\tan A=\frac{\sin A}{\cos A}=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}\]
    Hence, the required value of tan A is \[3/4\].


You need to login to perform this action.
You will be redirected in 3 sec spinner