If `int_0^1(sint)/(1+t)dx=alpha,` then the value of the integral `int_(4pi-2)^(4pi)(sint/2)/(4pi+2-t)dti s` `2alpha` (2) `-2alpha` (3) `alpha` (d) `-alpha`

If int_0^x(f(t))dt=x+int_x^1(t^2.f(t))dt+pi/4-1 , then the value of the integral int_-1^1(f(x))dx is equal to

If cos3theta=cos3alpha, then the value of sintheta can be given by +-sinalpha (b) sin(pi/3+-alpha) sin((2pi)/3+alpha) (d) sin((2pi)/3-alpha)

The value of the integral int_(-(3pi)/4)^((5pi)/4)((sinx+cosx)/(e^(x-pi/4)+1))dx (A) 0 (B) 1 (C) 2 (D) none of these

The value of int_0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (a) 1-cos alpha (b) 1+cos alpha (c) 1 (d) cos alpha

The value of the integral int_0^1(dx)/(x^2+2xcosalpha+1) is equal to (a) sinalpha (b) alphasinalpha (c) alpha/(2sinalpha) (d) alpha/2sinalpha

If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cotalpha)-cot^(-1)(tanalpha)+sin^(-1)(sinalpha)+cos^(-1)(cosalpha) is equal to (a) 2pi+alpha (b) pi+alpha (c) 0 (d) pi-alpha

IF sin ^(16) alpha = 1/5 then the value of (1) /(cos ^2 alpha) +(1)/( 1 + sin ^2 alpha) +(2)/(1+ sin ^4 alpha) + ( 4 )/( 1+ sin ^8 alpha) is equal to

The value of integral int_0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be (a) 3+2pi (b) 4-pi (c) 2+pi (d) none of these

If int_0^1 e^(x^2)(x-alpha)dx=0 , then (a) alphalt2 (b)= alphalt0 (c)="" 0ltalphalt1 (d)= alpha="0

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is