Question

If tan (cot x) = cot (tan x), then sin 2x =​

Answer 1

Answer:

sin 2x = 4/pi

Step-by-step explanation:

Given tan(cot x) = cot (tan x)

tan(cot x) = tan (pi/2-tan x)

cot x= pi/2-tan x

cot x + tan x = pi/2

cos x / sin x + sin x / cos x = pi/2

( cos^2 x + sin^2 x ) / sin x cos x = pi/2

1 / sin x cos x = pi/2

2 / 2sin x cos x = pi/2

2/ sin 2x = pi/2

sin 2x /2 = 2/pi

sin 2x = 4/pi