(a) Show that . (b) Hence, find the value of when…

MATHEMATICS · Subjective · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

(a) Show that sin⁡4θ+cos⁡4θ=1−2sin⁡2θcos⁡2θ\sin^{4}\theta+\cos^{4}\theta=1-2\sin^{2}\theta\cos^{2}\theta. (b) Hence, find the value of sin⁡4θ+cos⁡4θ\sin^{4}\theta+\cos^{4}\theta when sin⁡θcos⁡θ=310\sin\theta\cos\theta=\dfrac{3}{10}.

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