Prove that:`(sinx-siny)/(cosx+cosy)``=tan``(x-y)/2`

Prove that: tan^(-1){(a cosx-b sinx)/(b cosx+a sinx)} =tan^(-1)((a)/(b))-x

Prove that tan^(-1)((cosx-sinx)/(cosx+sinx))=(pi/4-x), x lt pi .

Prove that (1+sinx-cosx)/(1+sinx+cosx) +(1+sinx+cosx)/(1+sinx-cosx) =2 cosec x

Prove that (1+sinx-cosx)/(1+sinx+cosx) +(1+sinx+cosx)/(1+sinx-cosx) =2 cosec x

If x+y+z= pi/2 , prove that : cos(x-y-z) + cos(y-z-x) + cos (z-x-y)-4cosx cosy cosz=0

Prove that (cosx +cosy)^2+(sinx+siny)^2=4cos^2((x-y)/2)

What is the value of [(sin x + sin y)(sin x - sin y)]//[(cosx + cosy)(cosy- cosx)] ? [(sin x + sin y)(sin x - sin y)]//[(cosx + cosy)(cosy- cosx)] का मान क्या है?

y=(sinx)^(cosx)+(cosx)^(sinx)