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JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Mock Test - Trigonometric Functions

  • question_answer
    The value of expression \[\frac{2(sin{{1}^{o}}+sin{{2}^{o}}+sin{{3}^{o}}+\cdot \cdot \cdot \cdot +\sin {{89}^{o}})}{2(cos{{1}^{o}}+cos{{2}^{o}}+\cdot \cdot \cdot +cos{{44}^{o}})+1}\]Equals

    A) \[\sqrt{2}\]                    

    B) \[1/\sqrt{2}\]

    C) \[1/2\]               

    D) 0

    Correct Answer: A

    Solution :

    [a] Numerator =2\[2[(sin1{}^\circ +\sin 89{}^\circ )+(sin2{}^\circ +sin88{}^\circ )+..\]\[+(sin44{}^\circ +\sin 46{}^\circ )+sin45{}^\circ ]\] \[\Rightarrow \,\frac{Numerator}{Deno\min ator}\] \[=2[sin45{}^\circ \{2(cos44{}^\circ +cos43{}^\circ +...cos1{}^\circ )+1\}]\] \[=2\sin 45{}^\circ =\sqrt{2}\]


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