" ii) "x^(2)-2kx+7k-12=0[(4)/(sqrt(2 pi)x)sin(2 pi)/(10)(3

Prove that (i) "sin " (7pi)/(12) " cos " (pi)/(2) - "cos " *(7pi)/(12) " sin " (pi)/(4) = (sqrt(3))/(2) (ii) " sin " (pi)/(4) " cos " (pi)/(2) + "cos"(pi)/(4) " sin " (pi)/(12) = (sqrt(3))/(2) (iii) " cos " (2pi)/(3) " cos " (pi)/(4) - " sin " (2pi)/(3) " sin " (pi)/(4) =(-(sqrt(3) +1))/(2sqrt(2))

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

If sin x+sqrt(3)cos x=sqrt(2) then general solution of x 2n pi+(pi)/(12) 2n pi-(pi)/(12) 2n pi+(5 pi)/(12) 2n pi-(5 pi)/(12)

Show that int_(0)^(1//2)(x sin^(-1)x)/(sqrt(1-x^(2)))dx = (1)/(2)-(sqrt(3))/(12)pi

The solution of the system of equations sin x sin y=(sqrt(3))/(4),cos x cos y=(sqrt(3))/(4) are x_(1)=(pi)/(3)+(pi)/(2)(2n+k);n,k in Iy_(1)=(pi)/(6)+(pi)/(2)(k-2n);n,k in Ix_(2)=(pi)/(6)+(pi)/(2)(2n+k);n,k in Iy_(2)=(pi)/(3)+(pi)/(2)(k-2n);n,k in I

If sin x + sin ((pi)/(8) sqrt((1 - cos 2 x)^(2) + sin ^(2) 2 x)) = 0, x e [(5 pi)/(2), (7 pi)/(2)] , then x is

If [(cos (2pi)/7,-sin (2pi)/7),(sin (2pi)/7,cos (2pi)/7)]^k=[(1,0),(0,1)], then the least positive integral value of k, is

If tan((2 pi)/(3)-x)=(sin(2(pi)/(3)-sin2x))/(cos(2(pi)/(3)-cos2x)) where 0

Prove that the value of each the following determinants is zero: sin^(2)(x+(3 pi)/(2))quad sin^(2)(x+(5 pi)/(2))quad sin^(2)(x+(7 pi)/(2))sin(x+(3 pi)/(2))quad sin(x+(5 pi)/(2))quad sin(x+(7 pi)/(2))sin(x-(3 pi)/(2))quad sin(x-(5 pi)/(2))quad sin(x-(7 pi)/(2))

1+sinx + sin^2(x) + .... = 4+2sqrt3, 0ltxltpi, x!=pi, then x = 1) (pi)/(3), (pi)/(4) 2) (pi)/(4), (pi)/(6) 3) (2 pi)/(5), (pi)/(6) 4) (pi)/(3), (2 pi)/(3)