[" 12."(1)/(0)(1)/(4)root(3)(cos^(2)x+b^(2)sin^(2))=],[[" (a) "(pi)/(ab)," (d) "(x^(2))/(2ab)]]

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

The expression (tan^(4)x+2tan^(2)x+1)cos^(2)x, whenx =(pi)/(12) can be equal to (a)4(2-sqrt(3)) (b) 4(sqrt(2)+1) (c)16(cos^(2)pi)/(12) (d) 16(sin^(2)pi)/(12)

(lim)_(x rarr)(sin^(4)x-sin^(2)x+1)/(cos^(4)x-cos^(2)x+1) is equal to (a) 0( b) 1 (c) (1)/(3)(d)(1)/(2)

The value of sin^(-1)(cot(sin^(-1)((2-sqrt(3))/(4)+(cos^(-1)(sqrt(12)))/(4)+sec^(-1)sqrt(2))))(a)0( b) (pi)/(2)( c) (pi)/(3)( d) none of these

Solve 4cos x(2 -3sin^(2)x)+cos2x+1=0

If sin x+sin^(2)x=1, then cos^(8)x+2cos^(6)x+cos^(4)x=(A)2(B)1(C)3 (D) (1)/(2)

The range of (sin x-cos x)^(2)+cos^(2)((pi)/(4)-x) is A) [1,2] B) [-(1)/(4),(3)/(4)] C) [(3)/(4) , 1] D) [(3)/(2),2]

Let alpha=2tan^(-1)((1)/(2))+(sin^(-1)3)/(5) and beta=sin^(-1)((12)/(13))+cos^(-1)((4)/(5))+cos^(-1)((16)/(63)) be such that2sin alpha and cos beta are roots of the equation x^(2)-px+q=0, then (p-q) is

The values of x in (0, pi) satisfying the equation. |{:(1+"sin"^(2)x, "sin"^(2)x, "sin"^(2)x), ("cos"^(2)x, 1+"cos"^(2)x, "cos"^(2)x), (4"sin" 2x, 4"sin"2x, 1+4"sin" 2x):}| = 0 , are