Question

Tolong banget bantuannya
2tan / 1 + tan^x equivalen dengan
a. 2sinx
b. sin2x
c. 2cosx
d. cos2x
e. tan2x
note : ^=pangkat 2

Answer 1

(2tan x) / 1 + tan²x
=(2tan x) / 1 + (1 - sec²x)
=(2 tan x) / sec²x
=(2 (sin x / cos x)) / (1/cos²x)
= 2 sin x cos x
= sin 2x        B

Answer 2

2 tan x / ( 1 + tan^2 x ) 
= 2 ( sin x / cos x ) / [ 1 + ( sin^2 x / cos^2 x ) ]
Penyebut : 
= 1 + ( sin^2 x / cos^2 x )
= ( cos^2 x / cos^2 x ) + ( sin^2 x / cos^2 x )
= ( sin^2 x + cos^2 x ) / cos^2 x
= 1 / cos^2 x

2 ( sin x / cos x ) / [ 1 + ( sin^2 x / cos^2 x ) ]
= 2 ( sin x / cos x ) / [ 1 / cos^2 x ] 
= 2 sin x / ( 1 / cos x )
= 2 sin x cos x
= sin 2x ---> jawaban : B