Question

Question #0f589

Answer 1

`RHS=1-sin^2x/(1+cotx)-cos^2x/(1+tanx)`

`=1-sin^3x/(sinx+sinxcotx)-cos^3x/(cosx+cosxtanx)`

`=1-(sin^3x/(sinx+cosx)+cos^3x/(cosx+sinx))`

`=1-((sin^3x+cos^3x)/(cosx+sinx))`

`=1-((sinx+cosx)(sin^2x-sinxcosx+cos^2x))/(cosx+sinx)`

`=1-(sin^2x-sinxcosx+cos^2x)`

`=1-(1-sinxcosx)`

`=sinxcosx`

But `LHS=1-sinxcosx`

Hence `LGS!=RHS`

So it must be an equation which is

`1-sinxcosx=sinxcosx`

`=>2sinxcosx=1`

`=>sin2x=sin(pi/2)`

`=>2x=npi+(-1)^n(pi/2)`

`=>x=(npi)/2+(-1)^n(pi/4)" where "n in ZZ`