Why is 1/(1+((-sin x)/(1+cos x))^2) -= ((1+cos x)^2)/(sin^2 x+1+2 cos x+cos^2 x)?

Kaylynn Cook

Kaylynn Cook

Answered question

2022-11-19

Why is 1 1 + ( sin x 1 + cos x ) 2 ( 1 + cos x ) 2 sin 2 x + 1 + 2 cos x + cos 2 x ?

Answer & Explanation

Kristen Garza

Kristen Garza

Beginner2022-11-20Added 13 answers

If you multiply the numerator and the denominator by ( 1 + cos x ) 2 , you get:
1 1 + ( sin x 1 + cos x ) 2 = ( 1 + cos x ) 2 ( 1 + cos x ) 2 × 1 1 + ( sin x 1 + cos x ) 2 = ( 1 + cos x ) 2 ( 1 + cos x ) 2 ( 1 + ( sin x 1 + cos x ) 2 ) = ( 1 + cos x ) 2 ( 1 + cos x ) 2 + sin 2 x

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