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(sin5theta+sin2theta-sin theta)/(cos5the...

`(sin5theta+sin2theta-sin theta)/(cos5theta+2cos3theta+2cos^(2)theta+costheta)` is equal to

A

`tan theta`

B

`cot theta`

C

`cos theta`

D

`sin theta`

Text Solution

Verified by Experts

The correct Answer is:
A
`(sin5theta+sin2theta-sin theta)/(cos5theta+2cos3theta+2cos^(2)theta+cos theta)` ……………
`(2sin2theta cos3theta+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(2cos3theta+1))/(2cos^(2)theta(2cos3theta+1)) = tan theta`
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