If `a=xcos^2a+ ysin^2 A` then`(x-a)(y-a)+(x- y)^2 sin^2 A cos^2 A =`

If a=x cos^(2) alpha + ysin^(2) alpha " then " (x-a)(y-a)+(x-y)^(2)sin^(2) alpha cos^(2) alpha =

cos (x + y), sin (x + y), - cos (x + y) sin (xy), cos (xy), sin (xy) sin2x, 0, sin2y] | = sin2 (x + y)

(1)/(sin x.cos^(2)x)

int_(-pi)^(pi)sin^(2)x.cos^(2)x dx=

If xcos theta- y sin theta =a, x sin theta + y cos theta = b , prove that: x^(2) + y^(2) = a^(2) + b^(2) .

Show that (i) cos x+cos y=2 cos (x+y)/(2) cos (x-y)/(2) (ii) cos x-cos y=-2 sin (x+y)/(2) sin (x-y)/(2) (iii) sin x+sin y=2 sin (dot(x)+y)/(2) cos (x-y)/(2) (iv) sin x-sin y=2 cos (x+y)/(2) sin (x-y)/(2)

Prove that : (cos x + cos y)^2 + (sin x - sin y)^2 = 4 cos^2\ (x+y)/2

The value of cos y cos ((pi)/(2) - x) - cos ((pi)/(2) - y) cos x + sin y cos ((pi)/(2) - x) + cos x sin ((pi)/(2) - y) is zero if