If `int_0^1(sint)/(1+t)dt=alpha,` then the value of the integral `int_(4pi-2)^(4pi)(sin(t/2))/(4pi+2-t)dt` is (1)`2alpha` (2) `-2alpha` (3) `alpha` (4) `-alpha`

If overset(1)underset(0)int(sint)/(1+t)dt=alpha , then the value of the integral overset(4pi)underset(4pi-2)int("sin"(t)/(2))/(4pi+2-t)dt in terms of alpha is given by

The value of : int_(pi//6)^(5pi//6)sqrt(4-4sin^(2)t) dt , is

Evaluate the following integral: int_0^(pi//4)sin^3 2tcos2t\ dt

If int_0^1tan^(-1)xdx=alpha,t h e nint_0^(pi/4)tan^(-1)((2cos^2theta)/(2-sin2theta))sec^2thetadtheta is equal to: alpha (b) alpha/2 (c) 3alpha (d) 2alpha

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)

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)

Find the value of the expression 3[sin^(4)((3pi)/(2)-alpha)+sin^(4)(3pi+alpha)]-2[sin^(6)((pi)/(2)+alpha)+sin^(6)(5pi-alpha)] .

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

Integrate the following : int(sin4t+2t)dt

If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cotalpha)-cot^(-1)(tanalpha)+sin^(-1)(sinalpha)+cos^(-1)(c0salpha) is equal to 2pi+alpha (b) pi+alpha (c) 0 (d) pi-alpha