pROVE THAT (cotx - tan x)cosx=cosec1x-2sinx

Answer 1

LS = (cosx/sinx- sinx/cosx)(cosx)
= (cos^2 x - sin^2 x)/(sinxcosx) (cosx)
= (cos^2 x - sin^2 x)/sinx

RS = 1/sinx - 2sinx
= (1 - 2sin^2 x)/sinx
= (sin^2 x + cos^2 x - 2sin^2 x)/sinx
= (cos^2x - sin^2 x)/sinx
= LS