Question

Diketahui g(x) = g(x)=(sec 2x √(1-cos 4x ))/(cos^4 x (1-tan^4 x)
Tunjukkan: (sec 2x √(1-cos 4x ))/(cos^(4 ) x (1-tan^4 x )= √2 tan 2x sec 2x

Thanks atas jawabannya :)

Answer 1

(sec 2x √(1-cos 4x))/(cos^4x (1-tan^4x)) = √2 tan 2x sec 2x
ruas kiri :
(sec 2x √(1-cos 4x))/(cos^4x (1-tan^4x))
= (sec 2x √1-(1-2sin²2x))/ (cos^4 x(1-sin^4x/cos^4x)
= (sec2x √2.sin²2x)/ (cos^4x(cos^4x-sin^4x/cos^4x)
= √2.sec2x.sin2x / (cos²x-sin²x)(cos²x+sin²x)
= √2 sec2x sin 2x / cos 2x
= √2 sec2x tan2x =√2tan2x.sec2x