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If alpha=sin x cos^(3) x and beta=cos x ...

If `alpha=sin x cos^(3) x and beta=cos x sin^(3) x`, then :

A

`a-b gt0"for" x in(0,pi//4)`

B

`a-blt0` for `x in(0,pi//4)`

C

`a+blt0` for ` x in(0, pi//2)`

D

`a+blt0` for `x in(0,pi//4)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`a-b=sin x cosx(cos^(2)xx-sin^(2)x)=1/4sin4x`
`impliesa-bgt0"for" 0ltx lt(pi)/(4)`
Also, `a+bsinx cosx=1/2sin2x`
`impliesa+bgt0"for" 0lt2xltpii.e. 0ltx lt(pi)/(2)`
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