If `x` is any real number then show that `cos theta` cannot be equal to `x+ 1/x.`

If x is any non-zero real number, show that costheta' a n d ' sintheta can never equal to x+1/x ,

For any real number x , [x] denotes the largest integer less than or equal to and {x}=x-[x] The number of real solutions of 7[x]+23{x}=191 is (A) 0 (B) 1 (c) 2 (D) 3

For a real number x, let [x] denote the greatest integer less than or equal to x. Let f: R -> R be defined as f(x)= 2x + [x]+ sin x cos x then f is

Show that the statement . p : 'If x is a real number such that x^(3)+ 4x=0, then x=0' is true by Method of contradiction

Show that the statement . p : 'If x is a real number such that x^(3)+ 4x=0, then x=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=0' is true by Direct method

Show that the statement ''If x is real number such that x^(3)+4x=0 , then x=0'' is true by the method of contrapositive.

Statement -1 : If x in R, x ne 0 , then x^2 + 1/(x^(2)) cannot be equal to cos theta for any theta Statement -2 : Sum of a positive number and its reciprocal cannot be less than 2.

If sin(theta-x) = a, cos (theta-y) = b , then cos(x-y) may be equal to :

Let x and y be positive real numbers and theta an angle such that theta!=(npi)/2 for any integer ndot Suppose (sintheta)/x=(costheta)/y and (cos^4theta)/(x^4)+(sin^4theta)/(y^4)=(97sin2theta)/(x^3y+x y^3), then the value of x/y+y/x is