Let `2sin^2x+3sinx-2>0a n dx^2-x-2<0(x` is measured in radians). Then `x` lies in the interval `(pi/6,(5pi)/6)` (b) `(-1,(5pi)/6)` `(-1,2)` (d) `(pi/6,2)`

Find the number of solution(s) of following equations: (i) x^(2)-sinx-cosx+2=0 (ii) sin^(2)x - 2sinx - x^(2)-3=0, x in [0,2pi]

Which of the following set of values of x satisfies the equation 2^(2sin^2x-3sinx+1)+2^(2-2sin^2x+3sinx)=9? (a) x=npi+-pi/6,n in I (b) x=npi+-pi/3, n in I (c) x=npi,n in I (d) x=2npi+pi/2,n in I

int(2sinx)/(3+sin2x)\ dx

Evaluate the value of ("lim")_(n vec pi/2 )tan^2xsqrt((2sin^2x+3sinx+4)-sqrt(sin^2x+6sinx+2))

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

If (4cos^(2)x -2 sinx -3) sin x = 0 , then x is equal to (n in Z)

Prove that: (sinx-sin3x)/(sin^2x-cos^2x)=2sinx

Evaluate lim_(xto pi//2) tan^(2)x[sqrt(2sin^(2)x+3sinx+4)-sqrt(sin^(2)x+6sinx+2)]

Which of the following set of values of x satisfies the equation 2^((2 sin^(2) x-3sinx +1))+2^((2-2 sin^(2)x+3 sin x))=9 ?

Which of the following set of values of x satisfies the equation 2^((2 sin^(2) x-3sinx +1))+2^((2-2 sin^(2)x+3 sin x))=9 ?