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 2022-11-19 Answered
Why is 1 1 + ( sin x 1 + cos x ) 2 ( 1 + cos x ) 2 sin 2 x + 1 + 2 cos x + cos 2 x ?
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Answers (1)

Kristen Garza
Answered 2022-11-20 Author has 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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