Express as sum or difference:`2cos((3theta)/2)cos((5theta)/2)`

Express as sum or difference: 2sin3thetacos4theta

Solve: 2cos^2theta-3costheta+1=0

Express as product: cos2theta-cos8theta

solve : 2cos^2theta+4sin^2theta=3

Find general solutions or solution as per given condition: costheta+cos5theta-2cos3theta=0

Prove that 8 sin^4(theta/2)-8sin^2(theta/2)+1=cos2theta

Prove the following identities,where the angles involves are acute angles for which the expressions are defined:(vii) (Sintheta-2Sin^3theta)/(2Cos^3theta-Costheta)=tantheta

Prove that cos((phi-theta)/2)-sinthetasin((phi+theta)/2)=costhetacos((phi+theta)/2)

Find general solutions or solution as per given condition: 2cos^2theta + 3costheta-2= 0

Solve 2cos^2 theta+3 sin theta=0