show that `(alpha+ycotalpha)(xcotalpha+ytanalpha)=(x+y)^2+4x ycot^2 2alpha`

Show that, (x tan alpha + y cot alpha)( x cot alpha + y tan alpha) = (x+y)^(2) + 4 xycot^(2) 2 alpha.

(x tan alpha+y cot alpha)(x cot alpha+y tan alpha)-4xy cos^(2)2 alpha=

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

Show that xcosalpha+asin^2alpha=p touches the parabola y^2=4a x if pcosalpha+asin^2alpha=0 and that the point of contact is (atan^2alpha,-2atanalpha)dot