" (iv) If "(sin alpha)/(a)=(cos alpha)/(b)," then prove that "a sin2 alpha+b cos2 alpha=b

If (sin alpha )/(a) = ( cos alpha )/(b) , then a sin 2alpha + b cos 2 alpha =

If (sin alpha)/(a)=(cos alpha)/(b), then a sin2 alpha+b cos2 alpha=

I : If (cos alpha )/(a)=(sin alpha )/(b) then a cos 2 alpha + b cos 2 alpha =a II : If (sin alpha )/(a) =(cos alpha )/(b) then a sin 2 alpha + b cos 2 alpha = a

If y = (2 sin alpha )/(1 + cos alpha + sin alpha) then, prove that (1 - cos alpha + sin alpha)/(1 + sin alpha) = y .

Prove that, (sin alpha + cos alpha)/(cos alpha-sin alpha)=tan2 alpha + sec 2 alpha

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

Q. Prove that from the equality sin^4 alpha/a+cos^4 alpha/b=1/(a+b) follows the relation; sin^8 alpha/a^3+cos^8 alpha/b^3=1/(a+b)^3.