# Solve the equation sec x - sec x sin^{2}x = cos x

Question
Solve the equation \sec x - \sec x sin^{2}x = \cos x

2020-11-08
Work with a left side.
Factor out $$\\sec x$$:
$$\sec x-\sec x\sin^{2}x=\sec x(1-\sin^{2}x)$$
Use the Pythagorean identity: $$\sin^{2}x+\cos^{2}x=1$$
$$\sec x-\sec x\sin^{2}x=\sec x(\cos^{2}x)$$
Use the reciprocal identity: $$\sec x=1/\cos x$$
$$\sec x-\sec x\sin^{2}x=1/\cos x(\cos^{2}x)$$
$$\sec x-\sec x\sin^{2}x=\cos x$$

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