`(s in5theta+s in2theta-s intheta)/(cos5theta+2cos3theta+2cos^2theta+costheta)` is equal to `t a ntheta` b. `costheta` c.`cottheta` d. none of these

Options

A. `tan theta`
B. `cos theta`
C. `cot theta`
D. none of these

Explanation

LHS`=(2sin 2 theta cos 3 theta+sin 2 theta)/(2 cos 3 theta,cos 2 theta+2 cos 3 theta+2 cos ^(2)theta)=(sin 2theta[2 cos 3 theta+1])/(2[cos 3 theta(cos 2 theta+1)+(cos ^(2)theta)])`
`=(sin2 theta[2 cos 3 theta+1])/(2[cos 3 theta(2 cos ^(2)theta)+cos^(2)theta])=(sin2 theta(2 cos 3 theta+1))/(2 cos^(2)theta(2 cos 3 theta+1))=tan theta`