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Question

Evaluate : cos1x+sin1x2=π6

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Solution

cos1x+sin1x2=π6
cos1x=π6sin1x2
Let sin1x2=θx2=sinθx=2sinθ
cos1x=π6θ

x=cos(π6θ)

x=cosx6cosθ+sinπ6sinθ

x=32cosθ+12sinθ

=321sin2θ+12sinθ

x=321x24+12x2

xx4=321x24

3x4=324x24
squaring both sides
9x216=316(4x2)

9x2=123x2

12x2=12

x2=±1
cos1x4+sin1x2=π6 so x1
x=1
Hence, the answer is 1.



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