[" 0) "(sec(y)^(-)3cos2x-y2 sigma^(-))/(1)],[" 1) "4x^(2)+5x+1]

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 - cos ^(-1) (y)/(2) =alpha then 4x^(2) -4xy cos alpha+ y^(3) is equzal to

If sec^(-1)(cos^(2)x-2cos x+3)+cos ec^(-1)(5^(cos ec^(2)y)+1)=(pi)/(2) Then sin^(2)x-cos^(2)y=

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

(i) Evaluate : sec (cos^(-1).(1)/(2)) (ii) slove the equations sin^(-1) x + sin^(-1) y = (2pi)/(3) and cos^(-1) x - cos ^(-1) y = (pi)/(3)

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

If Cos^(-1)x-Cos^(-1)(y/2)=alpha" then "4x^(2)-4xycosalpha+y^(2)=