Trigonometry — practice questions

94 curated practice questions from Trigonometry (Mathematics JEE Main, NTA Exams) — 30 medium, 4 hard, 60 easy. Every question includes the final answer free; step-by-step worked solutions with a free account.

• The value of ^ -1 ( ( 15 4 )-1 ( 4 ) ) is equal to
• Given that the inverse trigonometric function assumes principal values only. Let x , y be any two real numbers in [–1…
• In a A B C if b=2, E=30^ , then the area of the circumcircle of Δ ABC in square units is:
• The sides of a triangle are 8 cm, 10 cm and 12 cm. Then, the greatest angle is
• 8 3 8 5 8 7 8 is equal to
• If 1- A 1+ A + A A = 1 A , for all permissible values of A, then A may belongs to
• AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point…
• Given b+c 11 = c+a 12 = a+b 13 for a ABC with usual notation. If A = B = C , then the ordered triad (α, β, ) has a value
• The value of 3 20^ -4 20^ is
• Let ( a , b ) ⊂ (0, 2p) be the largest interval for which sin –1 (sinq) – cos –1 (sinq) > 0, q ∈ (0, 2p), holds. If a x…
• A person standing on the bank of river observes that the angle of elevation of the top of a tree on the opposite bank…
• cosec [2 ^ -1 (5)+ ^ -1 ( 4 5 ) ] is equal to
• If 2 x 3 4 , then ^ -1 ( 12 13 x+ 5 13 x ) is equal to
• If ^ -1 17 + ^ -1 4 5 - ^ -1 77 36 =0, 0 < α < 13, then sin –1 (sina) + cos –1 (cosa) is equal to
• In a ∆ABC, A 2 = 5 6 , C 2 = 2 5 , then
• If x + 1 x = 2 cos θ, then x 3 + 1 x ^ 3 =
• If tan 2 and tan 2 are the roots of the equation 8x 2 – 26x + 15 = 0 then cos (α + β) is equal to
• The sum of possible value of x for ^ -1 (x+1)+ ^ -1 ( 1 x-1 )
• The set of all values of k for which (tan –1 x ) 3 + (cot –1 x ) 3 = k π 3 , x ∈ R , is the interval
• The sides of triangle are sin α, cos α and 1+ for some 0< < 2 . Then the greatest angle of the triangle is
• In a ∆ PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P=1, then the angle R is equal to
• The triangle PQR of which the angles P, Q, R satisfy P = Q 2 R , is
• In a Δ ABC, if the sides are a =3, ~b =5 and c =4 , then 2 + 2 is equal to
• If π is equal to
• The value of ( cosec ^ -1 5 3 + ^ -1 2 3 ) is
• A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides…
• The two legs of a right triangle are sinθ + sin ( 3 2 - ) and cosθ – cos ( 3 2 - ) . The length of its hypotenuse is
• In any triangle ABC, if A = B 2 C then
• If tanα = m ~m +1 , tan β = 1 2 m+1 , then α + β is equal to
• If sin θ and cos θ are the roots of the equation ax 2 – bx + c = 0, then a, b and c satisfy the relation :
• If ^ -1 [( )^ 1 2 ]+ ^ -1 [( )^ 1 2 ]=x , then sin x =
• The number of solutions of cosθ + 3 sin θ = 5, 0 ≤ θ ≤ 5π, is
• The value of ^ -1 ( 1+ ^ 2 (2) -1 (2) )- ^ -1 ( 1+ ^ 2 ( 1 2 ) +1 ( 1 2 ) ) is equal to
• The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is
• Which of the following when simplified does not reduce to unity ?
• The number of values of in [0,2 ] for which 2 sin 3 - 7 sin 2 + 7 sin = 2, is:
• If 0 2+ 2+ 2+ + 2(1+ ) there being n number of 2's, is equal to
• Let S be the set of all solutions of the equation x [- 1 2 , 1 2 ] . Then _ x S 2 ^ -1 (x^ 2 -1 ) is equal to
• ^ -1 ( 1+ 3 3+ 3 )+ ^ -1 ( 8+4 3 6+3 3 ) is equal to
• If A= 3 4 , then 32 A 2 5 A 2 equals
• Minimum value of 5 sin 2 θ + 4 cos 2 θ is
• In 2 cos 2 θ + 3sin θ = 0, then the general value of θ is–
• The value of 1- ^ 2 15^ 1+ ^ 2 15^ is
• Let ( m , n are co-prime natural numbers) be a solution of the equation (2 ^ -1 x )= 1 9 and let a, b be the roots of…
• The value of ( _ n=1 ^ 19 ^ -1 (1+ _ p=1 ^ n 2 p ) ) is
• Let an ^ -1 y= an ^ -1 x+ an ^ -1 ( 2 x 1-x^ 2 ) , where Then a value of y is
• If tanα, tanβ are the roots of the equation x 2 + px + q = 0 (p ≠ 0), then
• A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (=a)…
• If x ∈ R and x ≠ 0, then which of the following is not possible ?
• In a triangle ABC if A B= a b c^ 2 then the triangle is
• Let e^ 105 x -e^ -105 x =4 , then the value of the cos x is
• In a triangle ABC, 2ca sin ( A - B + C 2 ) is equal to
• The possible values of θ ∈ (0, π) such that sin (θ) + sin (4θ) + sin (7θ) = 0 are
• If 0<x< 1 2 and ^ -1 x = ^ -1 x , then a value of ( 2 + ) is
• The value of 14 3 14 5 14 7 14 9 14 11 14 13 14 is equal to
• Let A and B denote the statements array l A: + + =0 B: x+ + =0 array If ( - )+ ( - )+ ( - )=- 3 2 , then
• If A = 2 sin 2 θ – cos 2θ, then A lies in the interval
• In a triangle PQR, if R = 2 . If tan ( P 2 ) and tan are the roots of ax 2 + bx + c = 0, a ≠ 0 then
• The value of ^ -1 [ 1+x^ 2 + 1-x^ 2 1+x^ 2 - 1-x^ 2 ], |x|< 1 2 , x 0, is equal to
• The solution of ^ -1 x- ^ -1 2 x= 3 is,
• If 3 sin θ – 5 cos θ = a, then 5 sin θ + 3 cos θ is equal to
• The domain of the function cosec –1 is
• ABCD is a trapezium such that AB and CD are parallel and BC ⊥ CD. If ∠ADB = θ, BC = p and CD = q, then AB is equal to
• The upper ( 3 4 ) th portion of a vertical pole subtends an angle ^ -1 ( 3 5 ) at a point in the horizontal plane…
• The value of cos 12° . cos 24° . cos 36° . cos 48° . cos 72° . cos 84° is
• If in a triangle ABC a ^ 2 ( C 2 )+ ^ 2 ( A 2 )= 3 b 2 , then the sides a, b and c
• A value of x satisfying the equation sin[cot –1 (1 + x )] = cos[tan –1 x ], is
• If ^ -1 x= cosec ^ -1 y , then ^ -1 ( 1 x )+ ^ -1 ( 1 y ) is equal to:
• If x= y , y= z and z= x , then the value of x is
• If sec A = 17 8 and cosec B = 5 4 ; if A, B lies in first quadrant then sec (A + B) is equal to
• If 0 ≤ x ≤ , then the solution of equation 16^ ^ 2 x +16^ 104^ 2 x =10 is given by x equal to
• Given below are two statements. STATEMENT - 1: If cosec - = a ^ 3 and - =b^ 3 then a^ 2 b^ 2 [a^ 2 +b^ 2 ]=1 …
• (2 ^ -1 1 5 + ^ -1 5 2 +2 ^ -1 1 8 ) is equal to
• The value of 2+ 2+ 2+2 8 . where 0< < 8 is equal to
• For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among…
• The value of ^ 3 ( 8 ) ( 3 8 )+ ^ 3 ( 8 ) ( 3 8 ) is :
• The set of values of x for which 3 x- 2 x 1+ 3 x 2 x =1 is
• If ^ -1 x- ^ -1 y 2 = , then 4 x 2 – 4 xy cos α + y 2 is equal to
• A solution of the equation cos 2 θ + sin θ + 1 = 0, lies in the interval
• If tanx. tany = a and x + y = π/6, then tanx and tany satisfy the equation
• In a trangle ABC, if cotA cotB cotC > 0, then the triangle is
• General solution of equation 3 cos θ + sin θ = 2 is
• Let S = x R : 0 If n ( S ) denotes the number of elements in S then
• Let a 1 = 1, a 2 , a 3 , a 4 , ...... be consecutive natural numbers. Then ^ -1 ( 1 1+a_ 1 a_ 2 )+ ^ -1 ( 1 1+a_ 2 a_ 3…
• Given below are two statements. STATEMENT - 1: 5 +3 ( + 3 )+3 lies between - 4 and 10. STATEMENT - 2: . array l -1 1 -1…
• A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It…
• The trigonometric equation sin –1 x = 2sin –1 a , has a solution for
• In a triangle A B C, a=4, b=3, A=60^ , then c is the root of the equation
• Let 0 2 and x = X cos θ + Y sin θ, y = X sin θ – Y cos θ such that x 2 + 4xy + y 2 = aX 2 + bY 2 , where a, b are…
• 2 - ( ^ -1 4 5 + ^ -1 5 13 + ^ -1 16 65 ) is equal to
• The sines of two angles of a triangle are equal to 5 13 99 101 . The cosine of the third angle can be : (Assume that…
• If II , are the roots of the equation 6 x^ 2 -5 x+1=0 , then the value of ^ -1 x+ ^ -1 is,
• If 2 1+ + = then 1+ - 1+ is equal to
• The general solution of tan ( 2 ) = 0 is

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