Trigonometric Ratios, Functions & Equations - 1 - Free MCQ Test with solutions

The angles of a triangle are as 1 : 2 : 7, then ratio of greatest side to least side is

If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is

If a = 4, b = 3 and A = 60^∘, then c is a root of the equation

If cos A + cos B = , then the sides of the triangle ABC are in

Number of solutions of the equation cos⁶x + tan²x + cos⁶x . tan²x = 1 in the interval [0, 2π] is-

If tan(cot x) = cot(tan x), then sin 2x =

If m and n(> m) are positive integers, the number of solutions of equation n|sin x| = m|cos x| in [0, 2π] is -

sin 3 θ = 4 sin θ sin 2 θ sin 4 θ in 0 ≤ θ ≤ π has

The general solution to the equation tan 2θ. tan θ = 1 is

The number of  pairs (x, y) satisfying the equations sin x + sin y = sin(x + y) and | x | + | y | = 1 is

If the equation sin θ (sin θ + 2 cos θ) = a has a real solution, then the shortest interval containing all possible values of ‘a’ is

The number of solutions of the equation  2(sin⁴ 2x + cos⁴ 2x) + 3 sin² x cos² x = 0 is

Solution to the equation tan pθ = cot qθ is

Range of sin2 x + 3 sin x + 2 is

Find the number of principal solution of the equation tan (7π cos x) = cot (7π sin x).

The solution set of (2 cos x– 1) (3 + 2 cos x) = 0 in the interval 0 ≤ x ≤ 2π is -

If sin² x + sin xy = – 1, then  the value of x, y is

Solution of the inequality sin²x – 5sinx + 6 < 0 is

If cos x . cos y = 1, then the value of  x and y  is