Verify if 1 -sin^2x/(1+cos x)=cos x?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll keep 1 to the left side and we'll move the fraction (sin x)^2/(1+cos x) to the right side:

cos x + (sin x)^2/(1+cos x) = 1

We'll multiply both sides by 1 + cos x:

cos x*(1+cos x) + (sin x)^2 = 1 + cos x

We'll remove the brackets:

cos x + (cos x)^2 + (sin x)^2 = 1 + cos x

But, from Pythagorean identity, we'll get:

(cos x)^2 + (sin x)^2 = 1

The expression will become a equality:

cos x + 1 = 1 + cos x

Since the LHS is equal to RHS, the given identity 1 -sin^2x/(1+cos x)=cos x is verified.

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