Find the interval of `alpha` for which `(alpha, alpha^2, alpha) and (3, 2, 1)` lies on same side of `x+y-4z+2=0`.

If sin 3 alpha =4 sin alpha sin (x+alpha ) sin(x-alpha ) , then

If sin (3alpha) /cos(2alpha) < 0 If alpha lies in

The real value of alpha for which the expression (1-sin alpha)/(1+2i sin alpha) is purely real is

The value of parameter alpha , for which the function f(x) = 1+alpha x, alpha!=0 is the inverse of itself

The values of alpha for which the equation alpha^2/(1-tan^2x)=(sin^2x+alpha^2-2)/(cos2x) has solution can be

If Delta_(1) is the area of the triangle with vertices (0, 0), (a tan alpha, b cot alpha), (a sin alpha, b cos alpha), Delta_(2) is the area of the triangle with vertices (a sec^(2) alpha, b cos ec^(2) alpha), (a + a sin^(2)alpha, b + b cos^(2)alpha) and Delta_(3) is the area of the triangle with vertices (0,0), (a tan alpha, -b cot alpha), (a sin alpha, b cos alpha) . Show that there is no value of alpha for which Delta_(1), Delta_(2) and Delta_(3) are in GP.

The number of value of alpha in the interval [-pi,0] satisfying sin alpha +int_(alpha )^(2alpha) cos 2 x dx =0 , then

Prove that |{: (1,alpha,alpha^2), (alpha,alpha^2, 1),(alpha^2, 1,alpha) :}|=-(1-alpha^3)^2

If alpha and beta are the roots of x^2 - p (x+1) - c = 0 , then the value of (alpha^2 + 2alpha+1)/(alpha^2 +2 alpha + c) + (beta^2 + 2beta + 1)/(beta^2 + 2beta + c)