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

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Answer 1 · 2017-02-22T10:05:42

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

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

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

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

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