If `xcosθ−ysinθ=a, xsinθ+ycosθ=b`, then show that `x^2+y^2=a^2+b^2`

If x=asecθcosϕy=bsecθsinϕandz=ctanθ, show that x^2/a^2 + y^2/b^2− z^2/c^2 =1

If x = a cosec θ, y = b cot θ, then the value of (x^2/a^2)−(y^2/b^2) = ………………..

If y= A cos 4x + Bsin 4x , A and B are constants then show that y_2 + 16y = 0

If a tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 makes intercepts h and k on the co-ordinate axes then show that a^(2)/h^(2)+b^(2)/k^(2)=1 .

If x = a cos θ and y = b sin θ, then b2x2 + a2y2 = …………… (1) a2b2 (2) ab (3) a4b4 (4) a2 + b2

If y = A cos 4 x + B sin 4 x, A and B are constants then Show that y_2 + 16y =0

Let =|2a_1b_1a_1b_2+a_2b_1a_1b_3+a_3b_1a_1b_2+a_2b_1 2a_2b_2a_2b_3+a_3b_2a_1b_3+a_3b_1a_3b_2+a_2b_3 2a_3b_3| . Expressing as the product of two determinants, show that =0. Hence, show that if a x^2+2h x y+b y^2+2gx+2fy+c=(l x+m y+n)(l^(prime)x+m^(prime)y+n),t h e n|a hgh bfgfc|=0.

If 2 (a ^(2) + b ^(2)) = (a+b)^(2), then show that a =b

If x=asectheta,y=btantheta, then the value of x^(2)/a^(2)-y^(2)/b^(2)= …….. .