If the straight line `xcosalpha+ysinalpha=p` touches the curve `(x^2)/(a^2)+(y^2)/(b^2)=1` , then prove that `a^2cos^2alpha+b^2sin^2alpha=p^2dot`

Show that the straight line xcosalpha+ysinalpha=p touches the curve x y=a^2, if p^2=4a^2cosalphasinalphadot

In A B C , prove that (a-b^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

If x cos alpha +y sin alpha = 4 is tangent to (x^(2))/(25) +(y^(2))/(9) =1 , then the value of alpha is

Prove that sin^2alpha-sin^4alpha= cos^2alpha-cos^4alpha

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

x=sqrt(a^2cos^2alpha+b^2sin^2alpha)+sqrt(a^2sin^2alpha+b^2cos^2alpha) then x^2=a^2+b^2+2sqrt(p(a^2+b^2)-p^2) , where p is equal to (a) a^2cos^2alpha+ b^2sin^2alpha (b) a^2sin^2alpha+b^2cos^2alpha (c) (1/2)(a^2+b^2+(a^2-b^2)cos2alpha) (d) (1/2)(a^2+b^2-(a^2-b^2)cos2alpha)

If sin alpha + cos alpha = b, then sin 2 alpha is equal to

If (cos^(4)alpha)/(cos^(2) beta) + (sin^(4)alpha)/(sin^(2)beta) = 1, prove that sin^(4)alpha + sin^(4) beta = 2 sin^(2) alpha sin^(2) beta

If cos (theta - alpha) = a and sin(theta - beta) = b (0 lt theta - alpha, theta - beta lt pi//2) , then prove that cos^(2) (alpha - beta) + 2ab sin (alpha - beta) = a^(2) + b^(2)