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

If x sin alpha=y cos alpha, prove that :(x)/(sec2 alpha)+(y)/(cos ec2 alpha)=x

"If "0ltalphaltpi/2 " and " sin alpha + cos alpha + tan alpha + cot alpha + sec alpha + cosec alpha = 7 " then " "show that " sin 2 alpha " is a root of " x^(2) - 44x - 36 = 0

If x sin ^3 alpha + y cos^3 alpha = sin alpha cos alpha and x sin alpha - y cos alpha =0 , then x^2 +y^2 is

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

If tan theta = (x sin alpha + y sin beta)/(x cos alpha + y cos beta), "prove that " x sin (theta - alpha) + y sin (theta - beta) = 0

If x sin ^ (3) alpha + y cos ^ (3) alpha = sin alpha cos alpha and x sin alpha-y cos alpha = 0 then x ^ (2) + y ^ (2) =

If x cos alpha + y sin alpha = x cos beta + y sin beta "then" (sin alpha - cos alpha - sin beta + cos beta)/(sin alpha + cos alpha - sin beta - cos beta)=