Solve the equation `2(cosx + cos 2x) + sin2x(1+2 cosx)= 2 sinx` for `x(-pi<=x<=pi)`

Solve the equation sin2x-12(sinx-cosx)+12=0

Solve the equation (sinx+cosx)^(1+sin2x)=2, when 0lt=xlt=pi

Solve the equation (sinx+cosx)^(1+sin2x)=2 , when 0 lexlepi

Solve the equation sin^2x(tanx+1)=3sinx(cosx-sinx)+3 .

Let 0ltalpha,beta,gammalt(pi)/2 are the solutions of the equations cosx=x,cos(sinx)=x and sin(cosx)=x respectively, then show that gammaltalphaltbeta .

Number of solutions of the equation log_("sinx + cosx") sqrt2 - (-1 + 2sin2x) = 0 where x in [0, 2pi] , is _______