Prove that `cos2alpha=2s in^2beta+4cos(alpha+beta)s inalphas inbeta+cos2(alpha+beta)`

The value of the determinant |{:(1,sin(alpha-beta)theta,cos (alpha-beta)theta),(a, sinalphatheta,cos alphatheta),(a^(2),sin(alpha-beta)theta,cos(alpha-beta)theta):}| is independent of

If cot (alpha + beta )=0 , then sin(alpha+2beta ) =

Prove that 2tanbeta+cotbeta=tanalphaimplies2tan(alpha-beta)=cotbeta .

If cosalpha+cosbeta=0=sinalpha+sinbeta, then prove that cos2alpha+cos2beta=-2cos(alpha+beta) .

Let y = f(x), f : R ->R be an odd differentiable function such that f'''(x)>0 and g(alpha,beta)=sin^8alpha+cos^8beta+2-4sin^2alpha cos^2 beta If f''(g(alpha, beta))=0 then sin^2alpha+sin^2beta is equal to

If alpha,beta are roots of x^2-px+q=0 then find the quadratic equation whose roots are ((alpha^2-beta^2)(alpha^3-beta^3)) and alpha^2beta^3+alpha^3beta^2

If sin(theta+alpha)=aandsin(theta+beta)=b , then prove that cos2(alpha-beta)-4abcos(alpha-beta)=1-2a^(2)-2b^(2) .

cos^(2) alpha +cos^(2) beta +cos^(2) gamma is equal to

If 3 sin alpha=5 sin beta , then (tan((alpha+beta)/2))/(tan ((alpha-beta)/2))=