How can I solve this problem?Please,help.

Prove that,(cos8theta+6cos6theta+13cos4theta+8cos2theta)/(cos7theta+5cos5theta+8cos3theta)=2costheta

1 Answer
Dec 20, 2017

LHS
=(cos8theta+6cos6theta+13cos4theta+8cos2theta)/(cos7theta+5cos5theta+8cos3theta)

=(2costheta(cos8theta+6cos6theta+13cos4theta+8cos2theta))/(2costheta(cos7theta+5cos5theta+8cos3theta))
=(2costheta(cos8theta+6cos6theta+13cos4theta+8cos2theta))/(2costhetacos7theta+5*2costhetacos5theta+8*2costhetacos3theta)

=(2costheta(cos8theta+6cos6theta+13cos4theta+8cos2theta))/(cos8theta+cos6theta+5cos6theta+5cos4theta+8cos4theta+8cos2theta)

=(2costheta(cos8theta+6cos6theta+13cos4theta+8cos2theta))/(cos8theta+6cos6theta+13cos4theta+8cos2theta)

=2costheta=RHS