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Let f(x)=sin^6x+cos^6x+k(sin^4x+cos^4x) ...

Let `f(x)=sin^6x+cos^6x+k(sin^4x+cos^4x)` for some real number `kdot` Value of `k` for which `f(x)` is constant for all values of `x` is `-1/2` (b) `1/2` (c) `1/4` (d) `-3/2` All real numbers `k` for which the equation `f(x)=0` has solution lie in `[-1,0]` (b) `[0,1/2]` (c) `[-1,-1/2]` (d) none of these Number of values of `k` for which `f(x)=0` is an identity is (a) 0 (b) 1 (c) infinite (d) none of these

A

0

B

1

C

infinite

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(1-3sin^2xcos^2x)+k[1-2sin^2xcos^2x]=0` is an identity,
i.e., `(1+k)-(3+2k)sin^2xcos^2=0` is an identity.
`rArr 1+k=and 3+2k=0`, which do not hold simultaneously.
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