Prove the identity: 1 1 − sin ⁡ x + 1 1 + sin ⁡...

aangenaamyj

aangenaamyj

Answered

2022-07-15

Prove the identity:
1 1 sin x + 1 1 + sin x = 2 sec 2 x

Answer & Explanation

karburitc

karburitc

Expert

2022-07-16Added 7 answers

1 1 sin x + 1 1 + sin x = 2 sec 2 x
1 1 sin x ( 1 + sin x ) 1 + sin x + 1 ( 1 + sin x ) ( 1 sin x ) ( 1 sin x )
= 1 + sin x + 1 sin x 1 sin 2 x = 2 cos 2 x
sin 2 x + cos 2 x = 1
[ cos 2 x = 1 sin 2 x ]
= 2 sec 2 x
Jeffrey Jordon

Jeffrey Jordon

Expert

2022-08-01Added 2575 answers

Answer is given below (on video)

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