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Question

If x(π2,π2), then the value of tan1(tanx4)+tan1(3sin2x5+3cos2x) is

A
x2
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B
2x
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C
3x
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D
x
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Solution

The correct option is D x
tan1(tanx4)+tan1(3sin2x5+3cos2x)
tan1(tanx4)+tan1⎢ ⎢ ⎢ ⎢3.2tanx1+tan2x5+3.1tan2x1+tan2x⎥ ⎥ ⎥ ⎥
tan1(tanx4)+tan1[3tanx4+tan2x]
tan1⎢ ⎢ ⎢tanx4+3tanx4+tan2x1tanx4.3tanx4+tan2x⎥ ⎥ ⎥
tan1[16tanx+tan3x16+tan2x]
tan1[tanx(16+tan2x)16+tan2x]
=tan1(tanx)
=x

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