Question

(1+cosx/sinx)²= 1+cosx/1-sinx

Answer 1

Answer:

(1+cosx/sinx)^=1+cosx/1-sinx

{(sinx+cosx)/sinx}^=

{(sin^x+cos^x+2sinx.cosx)/sin^x}

{(1+2sinx.cosx)/sin^x}=

{(1+2sinx.cosx)/1-cos^x}=

{(1+2sinx.cosx)/(1-cosx)(1+cosx)=RHS

{(1+2sinx.cosx)(1+cosx)=1-cos^x/1-sinx

{1+2sinx.cosx}=sin^x/1-sinx+cosx-sinx.cosx

{1+2sinx.cosx}=sin^x/1+2sinx.cosx

sin^x=sin^x

LHS=RHS

*Hence proved