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`

Evaluate: int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2thetad theta

Evaluate: int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2thetad theta .

If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8)=alpha,alpha is constant, then f(tan^(-1)(t a n8) is equal to alpha (b) alpha-2 (c) alpha+2 (d) 2-alpha

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 f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8))=alpha,alpha is constant, then f(tan^(-1)(tan8)) is equal to (A) alpha (B) alpha-2 (C) alpha+2 (D) 2-alpha

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

If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal to 4 (b) 2sin^2alpha (c) -4sin^2alpha (d) 4sin^2alpha

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 tan theta=(sin alpha- cos alpha)/(sin alpha+cos alpha) , then:

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