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(sin 5theta+ sin 2theta- sin theta)/(cos...

`(sin 5theta+ sin 2theta- sin theta)/(cos5theta+2cos3theta+2cos^2theta+costheta)` is equal to

A

`tan theta`

B

`cos theta`

C

`cot theta`

D

none of these

Text Solution

Verified by Experts

LHS `=(2sin2thetacos3theta+sin2theta)/(2cos3theta.cos2theta+2cos3theta+2cos^(2)theta) = (sin2theta[2cos3theta+1])/(2[cos3theta(cos2theta+1)+(cos^(2)theta)]`
`=(sin2theta[2cos3theta+1])/(2[cos3theta(2cos^(2)theta)+cos^(2)theta]) = (sin2theta[2costheta+1])/(2[cos3theta(cos2theta+1)+(cos^(2)theta)]`
`=(sin2theta[2cos3theta+1])/(2[cos3theta(2cos^(2)theta)+cos^(2)theta]) = (sin2theta(2cos3theta+1))/(2cos^(2)theta(2cos3theta+1))=tantheta` Ans.
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