If sin theta + cos theta =p, what is sin^2 theta + cos^4theta in terms of p ?

1 Answer
Feb 22, 2017

1-((p^2-1)/2)^2

Explanation:

(sintheta+costheta)^2= 1+2sinthetacostheta = p^2

so

sinthetacostheta = (p^2-1)/2

now

sin^2theta+cos^4theta=sin^2theta+(1-sin^2theta)cos^2theta=1-sin^2thetacos^2theta

and putting all together

sin^2theta+cos^4theta = 1-((p^2-1)/2)^2