Verify the identity 1 cos xsin x sin x1 cos x 2 csc xSolut

Verify the identity. 1 cos x/sin x + sin x/1 cos x = 2 csc x

Solution

1 cos x/sin x + sin x/1 cos x = 2 csc x

LHS : (1 cos x)/sin x + sin x/(1 cos x)

Take LCD = sinx( 1-cosx)

: [( 1 - cosx)^2 +sin^2x ]/sinx(1 -cosx)

[ 1+cos^2x -2cosx + sin^2x]/sinx(1-cosx)

(2- 2cosx)/sinx(1-cosx)

2(1-cosx)/sinx(1-cosx)

2/sinx

2cscx

RHS