`a)`` VP =(Sin^3x+ Cos^3x)/(Sinx+ Cosx)`
`= ((Sinx+ Cosx)( Sin^2x+ Cos^2x- sin x. cosx))/(Sinx+ Cosx)`
`= Sin^2x+ Cos^2x- sin x. cosx`
`= 1- sin x. cosx =VP (đpcm)`
`b)` `VP =(Sin^2x - Cos^2x)/(1+ 2Sinx. Cosx)`
`= ((Sinx+ Cosx)(Sinx- Cosx))/(Sinx+ Cosx)^2`
`= (Sinx- Cosx)/ (sin x + cosx)`
`= (Sinx- Cosx)/cosx : (Sinx + Cosx)/ cos x `
`= (tanx -1)/(1+ tan x) = VP(đpcm)`
`c)` `VT=(1+ cot x). Sin^3x+ (1+ tan x). cos^3x `
`= sin^3x+ sin^3x .cosx/sinx+ cos^3x+cos ^3x.sinx/cosx `
`= sin^3x+ sin^2x .cosx+ cos^3x+cos ^2x.sinx `
`= sin^2x(sin x + cosx)+ cos^2x (cosx+ sinx)`
`=cosx + sinx= VP (đpcm) `
`d)` `VT=((Sinx + Cosx)^2-1)/(cotx - Sinx. Cosx)`
`= ((Sin^2x+ Cos^2x+ 2Sin x. cosx)-1 )/(cot x - Sinx. Cosx)`
`= \(1+ 2Sin x. cosx -1 )/ (cosx/sinx - sin x .cosx)`
`= \(2Sinx. Cosx)/ (Cosx (1/sinx- sinx)`
`= \(2Sinx. Cosx)/ (Cosx.(1-sin^2x)/sinx`
`= (2Sinx. Cosx)/ ((Cos^3x)/(sinx))`
`=(2Sinx. Cosx. sin x)/ (Cos^3x)`
`= 2 tan^2x =VP(đpcm)`
`e)` `VT =((Sin^2x +2 Cos^2x)-1)/ cot ^2x`
`=(Sin^2x +2 Cos^2x - Sin^2x -Cos^2x)/cot^2x`
`= cos^2x /cot^2x = cos^2x . (sin^2x)/(cos^2x) `
`= sin^2x = VP (đpcm)`
`f)` `VT=(sin^2x-tan^2x)/(cos^2x- cot^2x)`
`= (sin^2x-(sin^2x)/(cos^2x))/(cos^2x- (cos^2x)/(sin^2x))`
`=(sin^2x. cos^2x-sin^2x)/(cos^2x).(sin^2x)/(cos^2x.sin^2x- cos^2x) `
`=Tan^2x . (sin^2x(cos^2x-1))/(cos^2x.(sin^2x-1))`
`=Tan^6x =VP (đpcm) `
`g)` `VT=Cos^4x - sin^4x = cos^2x- sin^2x= cos 2x =VP (đpcm)`
`h)` Ta có: `Cos^4x - 2cos^2x +1 = (cos^2x -1)^2= sin^4x` (Luôn đúng)
`->Cos^4x - 2cos^2x = sin^4x- 1 (đpcm)`
`i)` `VT= Sin^4x + sin^2x.cos^2x +cos^2x `
`= (sin^4x + cos^2x.sin^2x) + cos2x`
`= sin^2x(sin^2x + cos^2x ) + cos2x`
`= cos^2x + sin^2x`
`= 1 = VP (đpcm)`
`j)` `VT=(1- sin^2x.cos^2x)/( cos^2x ) - cos^2x `
`= (sin^2x + cos^2x - sin^2x.cos^2x)/( cos^2x ) - cos^2x `
`= Tan^2x +1 - sin^2x- cos^2x `
`= tan ^2x = VP (đpcm)`
