Verify trig identities Verify trig Identities 11 csc x 11

Verify trig. identities

Verify trig. Identities 1/1 - csc x - 1/1 + csx x = -2 tanx secx

46. 1/( 1 - cscx) - 1/(1+cscx) = -2tanxsecx

LHS: 1/( 1 - cscx) - 1/(1+cscx)

taking ( 1- cscx)( 1+cscx) as LCD

So,{ ( 1+cscx) - ( 1-cscx)}/( 1- cscx)( 1+cscx)

=2cscx/( 1-csc^2x)

= 2cscx( 1- 1/sin^2x)

= 2cscx *sin^2x/( sin^2x -1)

= 2cscx*sin^2x/(-cosx^2x

= -2sinx/cos^2x)

= -2tanxsecx

RHS