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  5. Introduction to Trigonometry

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

  • question_answer
    If  \[\sin \theta +\cos \theta =a\] and \[\sec \theta +\cos ec\theta =b,\] then the value of \[b({{a}^{2}}-1)\]is _____.

    A) \[2a\]                           

    B) \[3a\]               

    C)  \[0\]                

    D)         \[2ab\]            

    Correct Answer: A

    Solution :

    We have, \[sin\,\theta +cos\,\theta =a\] and \[sec\,\theta +cosec\,\theta =b\] Now, \[b({{a}^{2}}-1)=\left( \frac{1}{\cos \theta }+\frac{1}{\sin \theta } \right)\] \[({{\sin }^{2}}\theta +{{\cos }^{2}}\theta +2\sin \theta \cos \theta -1)\] \[=\frac{\sin \theta +\cos \theta }{(\sin \theta \cos \theta )}\times (2\sin \theta \cos \theta )=2a\]


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