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If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(...

If `f(x)=x^(11)+x^9-x^7+x^3+1` and `f(sin^(-1)(sin8)=alpha,alpha` is constant, then `f(tan^(-1)(t a n8)` is equal to `alpha` (b) `alpha-2` (c) `alpha+2` (d) `2-alpha`

A

`alpha`

B

`alpha -2`

C

`alpha + 2`

D

`2 - alpha`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x) + f(-x) = 2`
Now `(sin^(-1) (sin 8)) = 3pi - 8 = y`
And `(tan^(-1) (tan 8)) = (8 - 3pi) = -y`
Hence, `f(y) + f(-y) = 2`
Given `f(y) = alpha`, we have `f(-y) = 2 - alpha`
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