Show that `sec^2theta=(4xy)/(x+y)^2` is possible only if x = y

Is costheta=(x+y)/(x-y) possible if x > y > 0?

Show that (a+b)^2=4ab sin^2theta is possible only when a= b.

Show that (a+b) ^2=4ab cos^2theta is possible if a=b

Is costheta=(x^2-y^2)/(x^2+y^2) possible if x, y in R and 0 < theta < 90^@ ?

Solve : sec4theta-sec2theta=2

Show that the straight line 3x + 4y = 20 touches the circle x ^2 + y ^2 = 16.

If a cos theta +bsin theta=x and a sin theta-b cos theta = y then prove that a^2+b^2=x^2+y^2

Show that x + y = 1 is the equation of the line of a diameter of the circle x ^2 + y ^2 - 4x + 2y + 1 = 0

Without solving the equations show that the straight lines 4x - y + 2 = 0, 3x + 2y -1 = 0 and x - 3y + 3 = 0 are concurrent.