If pi/2 < `alpha` < 3 pi/2 then the modulus argument of `(1+cos 2alpha)+i sin2alpha`

Prove that pi/2 le sin ^(-1) x +2 cos^(-1) x lt (3 pi)/(2)

If a r g(z)<0, then a r g(-z)-"a r g"(z) equals pi (b) -pi (d) -pi/2 (d) pi/2

The value of (cos"" (pi)/(2)+isin ""(pi)/(2))(cos ((pi)/(2^2))+isin((pi)/(2^2))) (cos ((pi)/(2^3))+isin((pi)/(2^3)))" ………."oo is

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-pi/2,pi/4) (b) (0,pi/2) (-pi/2,pi/2) (d) (pi/4,pi/2)

Range of tan^(-1)((2x)/(1+x^2)) is (a) [-pi/4,pi/4] (b) (-pi/2,pi/2) (c) (-pi/2,pi/4) (d) [pi/4,pi/2]

tan^(-1)[(cosx)/(1+sinx)] is equal to pi/4-x/2,forx in (-pi/2,(3pi)/2) pi/4-x/2,forx in (-pi/2,pi/2) pi/4-x/2,forx in (-pi/2,pi/2) pi/4-x/2,forx in (-(3pi)/2,pi/2)