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JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Trigonometrical ratios of sum and difference of two and three angles

  • question_answer
    If \[\frac{\pi }{2}<\alpha <\pi ,\,\text{ }\pi <\beta <\frac{3\pi }{2};\] \[\sin \alpha =\frac{15}{17}\] and \[\tan \beta =\frac{12}{5}\], then the value of \[\sin (\beta -\alpha )\] is [Roorkee 2000]

    A) -171/221

    B) -21/221

    C) 21/221

    D) 171/221 

    Correct Answer: D

    Solution :

    Given, \[\sin \alpha =\frac{15}{17},\tan \beta =\frac{12}{5}\] \[\Rightarrow \cos \alpha =\frac{8}{17},\sin \beta =\frac{12}{13}\]and \[\cos \beta =-\frac{5}{13}\] Þ \[\pi <\beta <\frac{3\pi }{2}\], \[\therefore \cos \beta =-\frac{5}{13}\] \[\sin (\beta -\alpha )=\sin \beta \cos \alpha -\cos \beta \sin \alpha \] = \[\frac{171}{221}\].


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