verify the identity costheta1tan2thetacosthetaSolutioncosthe

verify the identity cos(theta)/1+tan^2(theta)=cos(theta)

Solution

cos(theta)/1+tan^2(theta)=cos(theta)

LHS : cos(theta)/(1+tan^2(theta))

we know that 1+tan^2(theta) = sec^2(theta)

So, cos(theta)/(1+tan^2(theta)) = cos(theta)/sec^2(theta)

=cos^3(theta)