Show that `sin^(2)x=p+1/p` is impossible if x is real.

Show that the equation sintheta=x+1/x is not possible if x is real.

Prove that the equation : cos theta= x+1/x is impossible if x be real.

Show that the statement p: “If x is a real number such that x^3 + 4x = 0 , then x is 0” is true by method of contradiction.

Show that the statement p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by method of contrapositive.

Show that the statement p: “If x is a real number such that x^3 + 4x = 0 , then x is 0” is true by direct method.

Let F(x) be an indefinite integral of sin^(2)x Statement-1: The function F(x) satisfies F(x+pi)=F(x) for all real x. because Statement-2: sin^(2)(x+pi)=sin^(2)x for all real x.

If the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

Events A, B, C are mutually exclusive events such that P (A) = (3x+1)/3, P (B) =(1-x)/4 and P (C) =(1-2x)/2 . The set of possible values of x are in the interval :

Given p(x) =x^4 +ax^3 +bx^2+cx +d such that x = 0 is the only real root of P'(x) =0. If P(-1) < P(1), then in the interval [-1,1]

If p tan theta = tan p theta , then show that : (sin^2 p theta)/(sin^2 theta)= (sin p^2)/(1+(p^2-1)sin^2 theta) .