If `cos^4x/cos^2y+sin^4x/sin^2y=1` then prove that `cos^4y/cos^2x+sin^4y/sin^2x=1`

If cos^(-1)x+cos^(-1)y=pi/2 then prove that cos^(-1)x=sin^(-1)y

If (cos ^ (4) x) / (cos ^ (2) y) + (sin ^ (4) x) / (sin ^ (2) y) = 1 then prove that (cos ^ (4) y) / (cos ^ (2) x) + (sin ^ (4) y) / (sin ^ (2) x) = 1

If cos^(-1)x//2+cos^(-1) y//3=theta," prove that "9x^(2)-12xy cos theta+4y^(2)=36sin^(2) theta

If sin x + sin y + sin z = 0 and cos x + cos y + cos z = 0 then prove that cot (x+y)/2 = cot z and cos (x-y)/2 = pm 1/2

If (cos x)/(cos y)=a and (sin x)/(sin y)=b, then (a ^(2)-b^(2))*sin^(2)y =......

If cos^(-1)((x)/(2))+cos^(-1)((y)/(3))=theta, prove that 9x^(2)-12xy cos theta+4y^(2)=36sin^(2)theta

If cos x + cos y =(1)/(3) and sin x + sin y=(1)/(4) prove that tan ((x+y)/(2))=(3)/(4)