" (vii) "cos theta cos(theta)/(2)-cos3 theta cos(9 theta)/(2)=sin7 theta sin8 theta

Prove that: cos theta(cos theta)/(2)-cos3 theta(cos(9 theta))/(2)=sin7 theta s in8 theta

cos2 theta*cos(theta/(2))-cos3 theta*cos((9theta)/2)=sin5 theta*sin((5theta)/(2))

Prove that ( cos theta + cos 2 theta + cos 3 theta + cos 4 theta)/(sin theta + sin 2 theta + sin 3 theta + sin 4 theta)= cot ""(5theta)/(2).

Prove that: cos2theta.costheta/2-cos3theta.cos(9theta)/(2)=sin5theta.sin(5theta)/(2)

cos theta-cos3 theta+cos5 theta-cos7 theta=4sin theta sin4 theta cos2 theta

cos (2 theta) cos ((theta) / (2)) - cos (3 theta) cos ((9 theta) / (2)) = sin (5 theta) sin ((5 theta) / (2))

Simplify: (sin8 theta cos theta-sin6 theta cos3 theta)/(cos2 theta cos theta-sin3 theta sin4 theta)

(sin3 theta+cos3 theta)/(cos theta-sin theta)=1+2xx sin2 theta

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

(sin theta+cos theta)(1-sin theta cos theta)=sin^3 theta+cos^3 theta