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

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

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Answer 1 · 2017-02-22T10:05:42

$1 - {(\frac{p^{2} - 1}{2})}^{2}$ $1-((p^2-1)/2)^2$

Explanation:

${(sin θ + cos θ)}^{2} = 1 + 2 sin θ cos θ = p^{2}$ $(sintheta+costheta)^2= 1+2sinthetacostheta = p^2$

so

$sin θ cos θ = \frac{p^{2} - 1}{2}$ $sinthetacostheta = (p^2-1)/2$

now

${sin}^{2} θ + {cos}^{4} θ = {sin}^{2} θ + (1 - {sin}^{2} θ) {cos}^{2} θ = 1 - {sin}^{2} θ {cos}^{2} θ$ $sin^2theta+cos^4theta=sin^2theta+(1-sin^2theta)cos^2theta=1-sin^2thetacos^2theta$

and putting all together

${sin}^{2} θ + {cos}^{4} θ = 1 - {(\frac{p^{2} - 1}{2})}^{2}$ $sin^2theta+cos^4theta = 1-((p^2-1)/2)^2$

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

1 Answer

Explanation:

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If sinθ+cosθ=psin theta + cos theta =p, what is sin2θ+cos4θsin^2 theta + cos^4theta in terms of pp ?

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Explanation:

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