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Question

The value of tansin-135+cos-1313 is


A

617

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B

613

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C

135

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D

176

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Solution

The correct option is D

176


The explanation for the correct option

The given trigonometric expression: tansin-135+cos-1313.

Let us assume that sin-135=y

siny=35cosy=1-352sin2θ+cos2θ=1cosy=1-925cosy=25-925cosy=1625cosy=45

Thus, tany=sinycosy

tany=3545tany=34y=tan-134sin-135=tan-134

Let us assume that cos-1313=z

cosz=313sinz=1-3132sin2θ+cos2θ=1sinz=1-913sinz=13-913sinz=413sinz=213

Thus, tany=sinycosy

tanz=213313tanz=23z=tan-123cos-1313=tan-123

Therefore, tansin-135+cos-1313=tantan-134+tan-123

It is known that tan-1(A)+tan-1(B)=tan-1(A+B1-AB).

tansin-135+cos-1313=tantan-134+231-3423tansin-135+cos-1313=3×3+2×4121-12tansin-135+cos-1313=9+81212tansin-135+cos-1313=1712×2tansin-135+cos-1313=176

Hence, option D is correct.


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