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

Let `f(x) = sin^6x + cos^6x + k(sin^4 x + cos^4 x)` for some real number k. Determine(a) all real numbers k for which `f(x)` is constant for all values of x.

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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