Step-by-step explanation:
- sinx+sin(x+4x) =cot2x
- sinx+sinx cos4x+cosx sin4x=cot2x
sinx+sinx cos4x=sinx (1+cos4x) =
sinx (1-1+2(cos2x)^2) =2sinx (cos2x)^2
sin4x=2sin2xcos2x
2sinx(cos2x)^2+cosx+2sin2xcos2x=cot2x
2sinxcos2x(cos2x+2(cosx)^2)=cot2x
but 2(cosx)^2=cos2x+1
2sinxcos2x(cos2x+cos2x+1)=cos2x/sin2x
(2sinxsin2x)(2cos2x+1) =1
(4cosx(sinx)^2)(2cos2x+1) =1
