Question

prove the identity sex^2(x)=(4sin^2(x))/(sin^2(2x))

Answer 1

Uhm, do you mean \(sec^2x\)x? >_>

Answer 2

*\(\large sec^2(x)\)

Answer 3

yes

Answer 4

the equations is \[\sec ^{2}x=(4\sin ^{2}x)/(\sin ^{2}2x)\]

Answer 5

The numerator of the right side: 4sin^2 x = 2(1 - cos 2x)
The denominator of the right side:
sin^2 (2x) = (1 - cos^2 2x) = (1- cos 2x)(1 + cos 2x)
Simplify by (1 - cos 2x) -> The right side becomes:
2/(1 + cos 2x) = 2/2cos^2 x = 1/cos^2 x = sec^2 x. The identity is proven.

Answer 6

@Abhishek619