# Solve (sin x + cos x)(sin x + cos x)

Question
Solve $$(\sin x + \cos x)(\sin x + \cos x)$$

2021-03-09
Use Distributive Property of FOIL method to obtain:
$$\sin^{2}x+2\sin x\cos x+\cos^{2}x$$
Use the identity: $$\sin^{2}x+\cos^{2}x=1$$
$$=1+2\sin x\cos x$$
Use the double-angle identity: $$\sin^{2}x=2\sin x\cos x$$
$$=1+\sin2x$$

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