Question

If sinx - cosx=√2 sinx . prove that cot2x =1 . Answer only if you are sure. No spam please.

Answer 1

Step-by-step explanation:

(Sin x - Cos x) =√2sin x.

squRing both side

sin ^2x + cos^2x - 2 sin x cos x = 2 sin^2x

1 - 2sin x cos x = 2sin^2 x

2sin ^2x + 2 sin x cos x = 1

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

from equ 1 putting the value of sin

2 ( sinx - cos x) (sin x + cos x)/√2 =1

√2 ( sin^2x - cos^2) = 1

sin^2x - cos^2x = 1/√2

( 1 - cos^2x) - cos^2x = 1/√2 as sin^2x = 1-cos^2x

1- 2cos^2x = 1/√2

cos 2x = 1/√2. as 1-2cos^2x = cos2x

cos 2x =cos 45°

2x = 45/2°

so the value of cot 2x.

cot 2 × 45/2

cot 45°

= 1

hence proved