Prove that
` cos (pi + theta) = - cos theta`

Prove that (2 cos 2 theta+1)/(2 cos 2theta-1)=tan(60^@+theta) (tan 60^@-theta)

Prove that sin (30^(@) + theta) + cos (60^(@) + theta) = cos theta

Prove that cos theta + cos ((2pi)/(3)- theta)+ cos ((2pi)/(3)+ theta)=0

Prove that cos 8 theta cos 2 theta = cos^(2) 5theta- sin^(2) 3 theta

Prove that (cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2theta .

Prove the following: (sin theta - cos theta + 1 )/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)

If tan (phi /2)= sqrt((1+a)/(1-a)) tan"" theta/2," then prove that cos "phi=(cos theta-a)/(1-a cos theta)

Prove that : (2 cos 2^n theta + 1)/(2 cos theta +1) = (2 cos theta -1) (2 cos 2theta -1) (2 cos 2^2 theta -1) … (2 cos 2^(n-1) theta -1)

If 3tanthetatanphi=1 , then prove that 2cos(theta+phi) = cos(theta-phi)