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The expression (tan(x-(pi)/(2)).cos((3...

The expression
`(tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x))`simplifies to

A

`(1+cos^(2)x)`

B

`sin^(2)x`

C

`-(1+cos^(2)x)`

D

`cos^(2)x`

Text Solution

Verified by Experts

The correct Answer is:
B
`(tan.(x-(pi)/(2)).cos.((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x))`
`=((-cot)(sin x)+cos^(3)x)/((sin x).(-ct x))`
`=(-cos x + cos^(3)x)/(-cos x)`
`=1-cos^(2)x`
`=sin^(2)x`
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