[" 3.If "cos x+sin x=cos alpha-sin alpha," prove that,"],[qquad x-(pi)/(4)=2n pi+-(alpha+(pi)/(4))]

If cosx + sinx = cos alpha- sinalpha , prove that, x-pi/4 = 2npi +-(alpha + pi/4)

lim_(alpha rarr(pi)/(4))(sin alpha-cos alpha)/(alpha-(pi)/(4))

If (sin(x+alpha))/(cos(x-alpha))=(1-m)/(1+m), prove that tan((pi)/(4)-x)tan((pi)/(4)-alpha)=m

The expression (sin alpha+cos alpha)/(cos alpha-sin alpha) tan((pi)/(4)+alpha)+1, alpha in (-(pi)/(4), (pi)/(4)) simplifies to :

The expression (sin alpha+cos alpha)/(cos alpha-sin alpha) tan((pi)/(4)+alpha)+1, alpha in (-(pi)/(4), (pi)/(4)) simplifies to :

Prove the following : sin alpha+ sin (alpha+ (2 pi)/3)+ sin (alpha+ (4 pi)/3)=0 .

prove sin alpha+sin(alpha+(2pi)/3)+sin (alpha+(4pi)/3)=0