Test : Trigonometric Functions And Identities - 3 - Mathematics MCQ

 The number of solutions of the equation tan x - sec x = 2cos x lying in the interval [0.2π] is

 The number of values of x in [0, 5π] satisfying the equation 3cos 2x - 10cos x + 7 = 0 is

The smallest positive integral value of p for which the equation cos (p sin a) = sin(p cos x) in x has a solution in [0. 2π] is

If sin²θ - 2sinθ - 1 = 0 is to be satisfied for exactly 4 distinct values of θ ∈ [0,nπ], n ∈ N, then the least value of n is

If 2 tan2 x-5 sec x is equal to 1 for exactly 7 distinct values of    n ∈ N, then the greatest value of n is

The number of value of x ∈ [0, 2π] that satisfy cot x - cosec x = 2 sin x is

If sin a, 1 and cos 2a are in GP then a is equl to

 If 1/6 sinθ, cosθ and tanθ are in GP then the general value of θ is

 The general values of x for which cos 2x, 1/2 and sin 2x are in AP are given by

 The most general values of θ satisfying 

The most general solutions of the equation sec x - 1 - (√2 - 1) tan x are given by 

 The most general solutions of the equation sec²x √2(1 - tan²x) are given by

The most general values of x for which sin x + cos x,  are given by

 then the set of possible values of α is

Let α, β, be any two positive values of x for which 2cos x, |cosx| and 1- 3cos² x are in GP. The minimum value of |α-β| is

The sum of all the solutions of the equation cos x.cos  is

The values of x ∈ [-2π, 2π] such that  _{is purely imaginary, are given by}