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If y=tanxcos^2xthen (dy)/(dx) will be.....

If `y=tanxcos^2x`then `(dy)/(dx)` will be..

A

`1+2sin^(2)x`

B

`1-2sin^(2)x`

C

`1`

D

`2 sin^(2)x`

Text Solution

Verified by Experts

The correct Answer is:
B
`y=tanx cos(2)x`
`(dy)/(dx)=x^(2)(d)/(dx)(cos^(2)x)+cos^(2)x(d)/(dx)(tanx)`
`=1-2sin^(2)x`
Alter `:y=(sinx)/(cosx)xxcos^(2)x=sinx cosx`
`y=(1)/(2)sin2x`
`(dy)/(dx)=(1)/(2)xx2cos2x`
`=cos2x`
`=1-2sin^(2)x`
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