" 39.If "x sin alpha=y cos alpha," prove that "(x)/(sec2 alpha)+(y)/(cosec2 beta)=x

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

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

If tan alpha = (x sin beta)/(1-x cos beta) " and " tan beta = (y sin alpha)/(1-y cos alpha),"show that", (sin alpha)/(sin beta) = x/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 cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If x sec alpha+y tan alpha=x sec beta+y tan beta=a , then sec alpha*sec beta=

If p and q are the lengths of the perpendiculars from the origin to the straight lines x "sec" alpha + y " cosec" alpha = a " and " x "cos" alpha-y " sin" alpha = a "cos" 2alpha, " then prove that 4p^(2) + q^(2) = a^(2).

If p and p' are the distances of the origin from the lines x "sec" alpha + y " cosec" alpha = k " and " x "cos" alpha-y " sin" alpha = k "cos" 2alpha, " then prove that 4p^(2) + p'^(2) = k^(2).

If p and p' are the distances of the origin from the lines x "sec" alpha + y " cosec" alpha = k " and " x "cos" alpha-y " sin" alpha = k "cos" 2alpha, " then prove that 4p^(2) + p'^(2) = k^(2).