Question

Prove that sin 2x / 1 + cos 2x = tan x

Answer 1

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Answer 2

sin 2 x = 2 sin x cos x

cos 2 x = cos 2 x − sin 2 x

and using sin 2 x + cos 2 x = 1 we can also obtain

cos 2 x = ( 1 − sin 2 x ) − sin 2 x = 1 − 2 sin 2 x

and cos 2 x = cos 2 x − ( 1 − cos 2 x ) = 2 cos 2 x − 1

⇒ sin 2 x /1 + cos 2 x = 2 sin x cos x 1 + 2 cos 2 x − 1 = 2 sin x cos x /2 cos 2 x

= 2 sin x cos x /2cos x cos x

= sin x /cos x

= tan x

= right side