Question

Evaluate cos(tan-¹x)
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Answer 1

Answer:

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Step-by-step explanation:

Let cot

−1

x=y⟹x=coty⟹siny=

1+x

2

1

Let tan

−1

x

2

+1

1

=z⟹tanz=

1+x

2

1

So cosz=

1+(

x

2

+1

1

)

2

1

=

1+

x

2

+1

1

1

=

x

2

+1

x

2

+2

1

=

x

2

+2

x

2

+1

So cos[tan

−1

{sin(cot

−1

x)}]=cos[tan

−1

{siny}]=cos[tan

−1

1+x

2

1

]=cosz=

x

2

+1

x

2

+2