If `cos (theta - alpha) = a and sin(theta - beta) = b (0 lt theta - alpha, theta - beta lt pi//2)`, then prove that `cos^(2) (alpha - beta) + 2ab sin (alpha - beta) = a^(2) + b^(2)`

If cos(theta-alpha) = a and cos(theta-beta) = b then the value of sin^2(alpha-beta) + 2ab cos(alpha-beta)

If cos(alpha+beta)=0 then sin(alpha+2beta)=

If sin(theta+alpha)=aa n dsin(theta+beta)=b , prove that cos2(alpha-beta)-4a bcos(alpha-beta)=1-2a^2-2b^2

If sin(theta+alpha)=a, a n dsin(theta+beta)=b , prove that cos2(alpha-beta)-4a bcos(alpha-beta)=1-2a^2-2b^2

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

If 0 lt alpha, beta lt pi and they satisfy cos alpha + cosbeta - cos(alpha + beta)=3/2

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 , where 0lt=alpha, betalt= pi/2 , then find the values of tan(alpha+2beta) and tan(2alpha+beta) .

If alpha, beta are the roots of the equation a cos theta + b sin theta = c , then prove that cos(alpha + beta) = (a^2 - b^2)/(a^2+b^2) .

If alpha, beta are two different values of theta which satisfy is bc cos theta cos phi + ac sin theta sin phi=ab , then prove that (b^(2)+c^(2)-a^(2)) cos alpha cos beta+ ac sin alpha sin beta= a^(2)+b^(2)-c^(2) .