Question

`(sin5theta+sin2theta-sin tehta)/(cos5theta+2cos3theta+2cos^(2)theta+costheta)` is equal to
A. `tan theta`
B. `cos theta`
C. `cot theta`
D. none of these

Answer 1

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.