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

  • question_answer
    If \[\sqrt{(1-{{\cos }^{2}}\theta ){{\sec }^{2}}\theta }=k\,\tan \theta \]and \[0<\theta <90{}^\circ ,\] then k is:

    A) \[-1\]

    B) \[1\]

    C) \[2\]

    D) \[\frac{1}{2}\]

    Correct Answer: B

    Solution :

    [b]\[\sqrt{(1-{{\cos }^{2}}\theta )\,{{\sec }^{2}}\theta }=\sqrt{{{\sin }^{2}}\theta \cdot {{\sec }^{2}}\theta }\] \[[{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1]\]
    \[=\sqrt{{{\sin }^{2}}\theta \times \frac{1}{{{\cos }^{2}}\theta }}=\sqrt{{{\tan }^{2}}\theta }=\tan \theta \]
    \[=k\tan \theta \]
    On comparing, we get
    \[k=1\]


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