Show that `(pi)/(4), (pi)/(6)` and`(2pi)/(3)` cannot be the direction angles of any vector.

The direction angles of a vector with x-axis is (pi)/(4) with y -axis is (pi)/(3) .Find the direction angle of the vector with z-axis.

Show that int_(0)^((pi)/(2))(tan^(4)x)/(1+tan^(4)x)dx=(pi)/(4)

Evaluate int_((pi)/(6))^((pi)/(2))cosxdx .

Prove that sin (10pi)/(3) cos (13pi)/(6) + cos (8pi)/(3) sin (5pi)/(6) = -1

An ellipse is sliding along the coordinate axes. If the foci of the ellipse are (1, 1) and (3, 3), then the area of the director circle of the ellipse (in square units) is (a) 2pi (b) 4pi (c) 6pi (d) 8pi

If (sqrt(3))b x+a y=2a b touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then the eccentric angle of the point of contact is (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If the angles between the vectors veca and vecb,vecb and vecc,vecc an veca are respectively pi/6,pi/4 and pi/3 , then the angle the vector veca makes with the plane containing vecb and vecc , is

Show that cos (pi)/(15) cos""(2pi)/(15) cos"" (3pi)/(15) cos"" (4pi)/(15) cos"" (5pi)/(15) cos"" (6pi)/(15) cos"" (7pi)/(15) = (1)/(128) .