Trigonometry — practice questions

71 curated practice questions from Trigonometry (Mathematics JEE Advanced, NTA Exams) — 50 hard, 21 medium. Every question includes the final answer free; step-by-step worked solutions with a free account.

• Let cos (α + β) = 4 5 and let sin (α – β) = 5 13 , where 0 ≤ α, 4 . Then tan 2α is equal to
• If in ∆ ABC if A > B, tan A + tan B + tan C = 6 and tan A tan B = 2, then sin 2 A : sin 2 B : sin 2 C is
• Given cos 2 m θ cos 2 m + 1 θ .............. cos 2 n θ = 2^ n +1 2^ n - m +1 2^ m , where 2 m θ ≠ kπ, n, m, k ∈ I cos…
• The equation k cos x –3 sin x = k + 1 is solvable only if k belongs to the interval
• If P n = sin n θ + cos n θ where n ∈ W (whole number) and θ ∈ R (real number) If P n – 2 – P n = sin 2 θ cos 2 θ P λ …
• The value of x for which sin (cot –1 (1 + x )) = cos (tan –1 x ) is
• For any positive integer n , let S n : (0, ∞) → be defined by S_ n (x)= _ k=1 ^ n ^ -1 ( 1+k(k+1) x^ 2 x ), where for…
• In a triangle ABC, angle A is greater than angle B. if the measures of angles A and B satisfy the equation 3 sin x –4…
• 1 3 [ ^ 3 + ^ 3 ( 2 3 + )+ ^ 3 ( 4 3 + ) ] is equal to
• If =3 ^ -1 ( 6 11 ) and =3 ^ -1 ( 4 9 ) , where the inverse trigonometric functions take only the principal values…
• The number of solution in [0, π/2] of the equation cos 3x tan 5x = sin 7x is
• If x [0, 2 ], the number of solutions of the equation, sin 7x + sin 4x + sin x = 0 is :
• Let f (θ) = sin θ (sin θ + sin 3θ) then f
• A vessel containing water is given a constant acceleration ‘ a ’ towards the right along a straight horizontal path…
• If a = 18 5 18 7 18 , and x is the solution of the equation y = 2 [x] + 2 and y = 3 [x – 2], where [x] denotes the…
• The number of ordered pairs (α, β), where α, β ∈ (–π, π) satisfying cos (α – β) =1 and ( + )= 1 e is : (e > 1)
• If P n = sin n θ + cos n θ where n ∈ W (whole number) and θ ∈ R (real number) If P 1 = m, then the value of 4 (1 – P 6…
• 2 sin 2 β + 4 cos (α + β) sin α sin β + cos 2 (α + β) =
• The positive values of x satisfy the equation 8^ 1+| x|+ ^ 2 x+ | ^ 3 x |+ = 4 3 will be (where |cos x| < 1)
• If cos A = then the value of sin A 2 sin 5 ~A 2 is
• If 6 cos 2θ + 2 cos 2 ( 2 ) + 2 sin 2 θ = 0, – π θ =
• If in a triangle ABC, sin 2 A + sin 2 B + sin 2 C = 2, then the triangle is always
• Let f : (–1, 1) → R be such that f( 4 )= 2 2- ^ 2 for (0, 4 ) ( 4 , 2 ) . Then the values of f ( 1 3 ) is (are).
• The least value of cos 2 θ – (6 sin θ . cos θ) + 3 sin 2 θ + 2 is
• If P n = sin n θ + cos n θ where n ∈ W (whole number) and θ ∈ R (real number) The value of 2P 6 – 3P 4 + 10 is
• General solution of the equation, cot 3θ – cot θ = 0 is (n∈I)
• 5 sin 2 x + 3 sin x cos x + 6cos 2 x = 5 if (n ∈ I)
• If sinθ = 3sin (θ + 2α), then the value of tan (θ + α) + 2 tanα is
• The principal value of is
• If sinα, sin β and cosα are in G.P. then roots of the equation x 2 + 2x cot β + 1 = 0 are always
• The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1 has a solution, is :
• If 0 x 1+x^ 2 [ x ( ^ -1 x )+ ( ^ -1 x ) ^ 2 -1 ]^ 1 / 2 =
• If + = 2 and + = , then tan α equals :
• If |tan x| ≤ 1 and x ∈ [–π, π] then the solution set for x is
• The value of θ satisfying are 3 cos 2 θ – 2 3 sin θ cos θ – 3 sin 2 θ = 0 are (n∈I)
• If x ∈ [- 5 2 , 5 2 ], the greatest positive solution of 1 + sin 4 x = cos 2 3x is
• Given cos 2 m θ cos 2 m + 1 θ .............. cos 2 n θ = 2^ n +1 2^ n - m +1 2^ m , where 2 m θ ≠ kπ, n, m, k ∈ I cos 2…
• If cos x – sin x ≥ 1 and 0 ≤ x ≤ 2π then the solution set for x is
• A table tennis ball has radius (3/2) × 10 −2 m and mass (22/7) × 10 −3 kg. It is slowly pushed down into a swimming…
• If sin 4 x + cos 4 y + 2 = 4 sin x cos y, and 0 ≤ x, y ≤ π/2 then sin x + cos y is equal to :
• Given both θ and φ are acute angles = 1 2 , = 1 3 , then the value of θ + φ belongs to
• If 4 sin 2 x – 8 sin x + 3 ≤ 0, 0 ≤ x ≤ 2π, then the solution set for x is
• If sin x + cos y = a and cos x + sin y = b, then tan x-y 2 is equal to
• If k 1 = tan 27θ – tan θ and k _ 2 = 3 + 3 9 + 9 27 , then
• The number of all possible triplets ( a 1 , a 2 , a 3 ) such that a 1 + a 2 cos (2 x ) + a 3 sin 2 x = 0 ∀ x is
• Match the following for the trigonometric equation |x+ 1 4 |- |x- 1 4 | = cos πx, (n is an integer) : Column - I Column…
• The no. of real solutions of ^ -1 x(x+1) + ^ -1 x^ 2 +x+1 = 2 is
• Assertion : The function f (x) = min sin x, cos x takes the value 4 5 twice when x varies from 20 3 to 43 6 . Reason …
• For any y ∈ , let cot –1 ( y ) ∈ (0, π) and an ^ -1 (y) (- 2 , 2 ) . Then the sum of all the solutions of the equation…
• If we consider only the principal values of the inverse trigonometric functions then the value of ( ^ -1 1 5 2 - ^ -1 4…
• The number of real solutions of sin e x . cos e x = 2 x–2 + 2 –x–2 is
• For non-negative integer n , let f(n)= _ k=0 ^ n ( k+1 n+2 ) ( k+2 n+2 ) _ k=0 ^ n ^ 2 ( k+1 n+2 ) Assuming cos –1 x…
• Column - I Column - II ( a) ^ 2 52 1^ 2 - ^ 2 22 1^ 2 (p) 1 (B) ^ 2 3 5 + ^ 2 4 5 (Q) 3- 3 4 2 (C) sin 24° + cos 6° (R)…
• If m and n (> m) are positive integers, the number of solutions of the equation n |sin x| = m | cos x| in [0, 2π] is
• The number of values of x where the function f ( x ) = cos x + cos attains its maximum, is
• If is always greater than or equal to
• Given cos 2 m θ cos 2 m + 1 θ .............. cos 2 n θ = 2^ n +1 2^ n - m +1 2^ m , where 2 m θ ≠ kπ, n, m, k ∈ I sin 9…
• Let f_ n ( )= 2 (1 + sec θ) (1 + sec 2θ) (1 + sec 4θ)............ (1 + sec 2 n θ), then
• If ( )^ 2 = =3, then
• Considering only the principal values of the inverse trigonometric functions, the value of ( ^ -1 ( 3 5 )-2 ^ -1 ( 2 5…
• Consider three points P = (– sin( β – α ), – cos β ), Q = (cos( β – α ), sin β ) and R = (cos( β – α + θ ), sin( β – θ…
• The value of _ n=1 ^ 23 ^ -1 (1+ _ k=1 ^ n 2 k ) is
• sin x – cos 2 x – 1 assumes the least value for the set of values of x given by :
• If r > 0, –π ≤ θ ≤ π and r, θ satisfy r sin θ = 3 and r = 4 (1 + sin θ), then the number of possible solutions of the…
• Which of the following statements are possible with a, b, m and n being non-zero real numbers :
• If sin x + 7 cos x = 5 then cos (x – φ) = 1/ 2 if
• If cosα = 2 -1 2- , (0 < α < π,0 < β < π), then tan 2 2 is equal to
• Assertion : The numbers sin 18° and – sin 54° are the roots of same quadratic equation with integer co-efficients…
• Let O be the origin, and and be three unit vectors in the directions of the sides Q R , R P , P Q , respectively, of a…
• The total number of real solutions of the equation = ^ -1 (2 )- 1 2 ^ -1 ( 6 9+ ^ 2 ) is (Here, the inverse…
• If 2 sin x + 1 ≥ 0 and x ∈ [0, 2π], then the solution set for x is

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