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If `a=sinxcos^3x` and `b=cosxsin^3x` then

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If `a=sinxcos^3x` and `b=cosxsin^3x` 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)`
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1 Answer

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Correct Answer - 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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