If `cos^4alpha/x+sin^4alpha/y=1/(x+y)` then prove that the value of `(dy)/(dx)` is `tan^2alpha` .

If x= cos alpha+ i sin alpha, y = cos beta+ i sin beta, then prove that (x-y)/(x+y) =i (tan )(alpha-beta)/2

If x=cos alpha+i sin alpha,y=cos beta+i sin beta then prove that (x-y)/(x+y)=i(tan)(alpha-beta)/(2)

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

If (cos^4 alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1 ,then prove that (cos^4beta)/(cos^2alpha)+(sin^4beta)/(sin^2alpha)=1

If x sin alpha = y cos alpha, prove that : x/(sec 2alpha) + y/(cosec 2 alpha) = x

Show that x cos alpha+y sin alpha=p touches the parabola y^(2)=4ax if p cos alpha+a sin^(2)alpha=0 and that the point of contact is (a tan^(2)alpha,-2a tan alpha)

If" " tan theta = (sin alpha - cos alpha)/(sin alpha + cos alpha),"prove that",2 cos^(2) theta = 1 + sin 2 alpha.