If `y sinphi = x sin (2theta + phi)` show that `(x + y) cot (theta + phi) = (y-x) cot theta`.

If cos theta = n cos ( theta + 2 phi) "show that"(n+1) tan ( theta + phi)= (n-1) cot phi

If 2 tan theta = cot phi, "show that" cos(theta - phi) = 3 cos ( theta + phi).

If sin theta = k sin (theta + phi),"show that", tan(theta + phi) = (sin phi)/(cos phi -k).

(sin (theta + phi))/( sin theta cos phi) = cot theta tan phi +1.

If sin theta = x and sec theta = y, then cot theta is

"If" (a cos theta sec phi - x)/(a sin (theta + phi)) = (y - b sin theta sec phi)/(b cos (theta + phi)) = tan phi, "show that," x^(2)/a^(2) + y^(2)/b^(2) = 1.

If sin theta=k sin(theta+phi), show that tan(theta+phi)=(sin phi)/(cos phi-k)

If tan theta + tan phi = x "and" cot theta + cot phi = y, "prove that " cot ( theta + phi) = 1/x -1/y

If theta+phi=45^@ , prove that (cot theta-1) (cot phi-1) =2 .

If tan theta = (xsin phi)/(1-xcos phi) and tan phi = (y sin theta)/(1-y cos theta) show that x sin phi = y sin theta