Verify the following 10 1sin2x1cosx cosx 11 1sinx 1cscx c

Verify the following. 10 1-sin^2x/1-cosx = -cosx 11. 1/sinx - 1/cscx = cosx cotx 12. Sec^4x -tan^4x = 1+2tan^2x

10) we have given 1-sin²x/(1-cosx)=-cosx

LHS=1-sin²x/(1-cosx)=(1-cosx-sin²x)/(1-cosx) =(cos²x-cosx)/(1-cosx) =-cosx(1-cosx)/(1-cosx) =-cosx=RHS

the given equation is verified

11) we have given 1/sinx -1/cscx =cosx cotx

LHS=1/sinx -1/cscx =(cscx -sinx)/(sinx cscx) =(1/sinx -sinx)/(sinx cscx)=(1-sin²x)/(sin²x cscx)

=cos²x/(sin²x cscx)=cos²x/(sin²x *1/sinx)=cos²x/(sinx) =cosx*(cosx/sinx)=cosx*cotx =RHS

the given equation is verified

12) we have given sec⁴x-tan⁴x=1+2tan²x

LHS=sec⁴x-tan⁴x =(sec²x)²-tan⁴x =(1+tan²x)²-tan⁴x since sec²x-tan²x=1

=1+tan⁴x+2tan²x-tan⁴x

=1+2tan²x = RHS

the given equation is verified