cos(thetha)*cos(thetha/2) - sine(thetha)*sine(thetha/2) + sin(thetha)*cos(thetha/2) + cos(thetha)*sine(thetha/2) = cos(3*thetha/2) + sine (3*thetha/2) . Proof is needed to show LHS=RHS

Dear student

Cos (a+b) = cos a cos b - sin a sin b

Sin ( a+ b) = sin a cos b + cos a sin b

Apply these equations in the question

Lhs = cos ( theta + theta*0.5) + sin ( theta + 0.5 theta ) = RHS

HENCE PROVED

Regards