Question

(cosec x- sin x)( sec x- cos x)( tan x+ cot x )= 1​

Answer 1

Answer:

LHS = (cosec x - sin x)(sec x - cos x)(tan x + cot x)

= (1 / sin x - sin x)(1 / cos x - cos x)(tan x + 1 / tan x)

= (1 - sin²x)(1 - cos²x)(tan²x + 1) / (sin x * cos x * tan x)

= cos²x * sin²x * (tan²x + 1) / (sin x * cos x * tan x), noting sin²x + cos²x = 1

= cos²x * sin²x * sec²x / [sin x * cos x * (sin x / cos x)], noting tan²x + 1 = sec²x

= sin²x / sin²x, as sec²x = 1 / cos²x

= 1

= RHS

Hope it helps you