If `(sin^4 theta)/a+ (cos^4 theta)/b= 1/(a+b)`, prove that `(sin^12 theta)/a^5+ (cos^12 theta)/b^5= 1/(a+b)^5` .

If (sin^4 theta)/a+ (cos^4 theta)/b= 1/(a+b) , prove that (sin^(4n) theta)/a^(2n-1)+ (cos^(4n) theta)/b^(2n-1)= 1/(a+b)^(2n-1), n in N .

Prove that : sin 2 theta= 2sin theta cos theta .

If tan theta =a/b , prove that a sin 2 theta+b cos 2 theta=b .

Prove that : sin^8 theta- cos^8 theta= (sin^2 theta- cos^2 theta)(1-2 sin^2 theta cos^2 theta) .

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec theta .

Prove that : cos2 theta= cos^2 theta-sin^2 theta=1-2 sin^2 theta= 2 cos^2 theta-1 .

If (sin (theta+alpha))/(cos (theta-alpha))= (1-m)/(1+m) , prove that : tan (pi/4- theta) tan (pi/4- alpha)=m .

If tan (pi cos theta)= cot(pi sin theta) , prove that cos (theta-pi/4)= +- 1/(2 sqrt2) .

Prove that : sin(9-theta\)=cos(81+theta)

If int (sin 3 theta + sin theta ) cos theta e ^(sin theta ) d theta = (A sin ^(3) theta + B cos ^(2) theta + C sin theta + D cos theta +E)e^(sin theta)+F, then: