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

  • question_answer
    If \[0<\theta <\frac{\pi }{4},\] then the simplest from of \[\sqrt{1-2\sin \theta \cos \theta }\] is:

    A) \[\sin \theta -\cos \theta \]

    B) \[\cos \theta -\sin \theta \]

    C) \[\cos \theta +\sin \theta \]

    D) \[\sin \theta \,\cos \theta \]

    Correct Answer: B

    Solution :

    [b] \[\sqrt{1-2\sin \theta \cos \theta }=\sqrt{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta -2\sin \theta \cos \theta }\]\[=\sqrt{{{(cos\theta -sin\theta )}^{2}}}\]
    \[[{{a}^{2}}+{{b}^{2}}-2ab={{(a-b)}^{2}}and1=si{{n}^{2}}\theta +{{\cos }^{2}}\theta ]\]
    \[=\cos \theta -\sin \theta \]


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