PrepWiser › Learn › Mathematics › Trigonometric EquationsTrigonometric Equations — JEE Main PYQs & Practice Questions Trigonometric Equations is a Mathematics chapter in the JEE Main syllabus. This page brings together 51 previous-year and practice questions on Trigonometric Equations, organised into 2 topics: General Solutions and Equations Reducible to Quadratic. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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General Solutions The number of elements in the set S = { θ ∈ [ - 4π ,4π ]:3cos ²2θ + 6 cos 2θ - 10cos ²θ… The number of solutions of |cos x|=sin x, such that -4 π ≤ x ≤ 4 π is : The number of solutions of the equation x + 2tanx = π/2 in the interval [0, 2π] is : The number of values of x in the interval ( π/4,7π/4 ) for which 14 cos ec²x - 2sin ²x =… Let S=[-π, π/2)-{-π/2,-π/4,-(3 π)/4, π/4}. Then the number of elements in the set | A={θ… Let S={θ ∈[0,2 π]: 8^(2 sin ² θ)+8^(2 cos ² θ)=16} . Then n(s) + Σ_(θ ∈ S) ( sec ( π/4 +… If θ₁ and θ₂ be respectively the smallest and the largest values of θ in (0, 2π) - π… The number of elements in the set S={θ ∈[0,2 π]: 3 cos ⁴ θ-5 cos ² θ-2 sin ⁶ θ+2=0} is : If θ ε[-(7 π)/6, (4 π)/3], then the number of solutions of √3 cosec² θ-2(√3-1) cosec… All possible values of θ ∈ [0, 2π] for which sin 2θ + tan 2θ > 0 lie in : The general solution of sin x = 0 is: If 2 tan ² θ-5 sec θ=1 has exactly 7 solutions in the interval [0, (n π)/2], for the… The number of solutions of the equation 2 x+3 tan x=π, x ∈[-2 π, 2 π]-{ ± π/2, ± (3… The number of solutions of tan x = √3 in [0, 2π] is x. The number of solutions of the equation cos 2θ cos θ/2 + cos 5θ/2 = 2 cos³ 5θ/2 in [… The number of distinct real roots of | sin x, cos x, cos x; cos x, sin x, cos x; cos x… Let S₁ = { x ∈ [0,12π ]:sin ⁵x + cos ⁵x = 1} and S₂ = { x ∈ [0,8π ]:sin ⁷x + cos ⁷x = 1}… Let S={θ ∈(0, π/2): Σₘ₌₁⁹ sec (θ+(m-1) π/6) sec (θ+(m π)/6)=-8/√3}. Then The sum of the solutions x ∈ ℝ of the equation (3 cos 2 x+cos ³ 2 x)/(cos ⁶ x-sin ⁶… The number of solutions of sin⁷x + cos⁷x = 1, x∈ [0, 4π] is equal to Equations Reducible to Quadratic The number of solutions of the equation (4-√3) sin x-2 √3 cos ² x=-4/(1+√3), x ∈[-2 π… Let S be the sum of all solutions (in radians) of the equation sin ⁴θ + cos ⁴θ - sin θ… The number of solutions of the equation sin x = cos ²x in the interval (0, 10) is… Let S={x∈ [-π,π]:sin x(sin x+cos x)=a, a∈ ℤ}. Then n(S) is equal to: The number of solutions of sin ² x+(2+2 x-x²) sin x-3(x-1)²=0, where -π ≤ x ≤ π, is… If α,-π/2<α<π/2 is the solution of 4 cos θ+5 sin θ=1, then the value of tan α is Let α and β be two real roots of the equation (k + 1)tan²x - √2 . λtanx = (1 - k), where… The number of solutions of the equation 32^(tan ²x) + 32^(sec ²x) = 81, 0 ≤ x ≤ π/4 is : Number of solutions of √3 cos 2θ+8 cos θ+3√3=0,θ∈ [-3π,2π] is : The sum of all values of θ ∈[0,2 π] satisfying 2 sin ² θ=cos 2 θ and 2 cos ² θ=3 sin θ is If θ ∈[-2 π, 2 π], then the number of solutions of 2 √2 cos ² θ+(2-√6) cos θ-√3=0, is… If √3 (cos ²x) = (√3 - 1)cos x + 1, the number of solutions of the given equation when x… The sum of all the integral values of p such that the equation 3 sin² x+12 cos x-3=p,x∈… The number of roots of the equation, (81) sin²x + (81) cos²x = 30 in the interval [ 0, π… The number of solutions of the equation 4 sin ² x-4 cos ³ x+9-4 cos x=0 ; x ∈[-2 π, 2 π]… The number of elements in the set {x∈ [0,180°]:tan (x+100°)=tan (x+50°)tan x tan… If S={θ∈ [-π,π]:cos θ cos 5θ/2=cos 7θ cos 7θ/2}, then n(S) is equal to ____ . Let S={θ∈ (-2π,2π):cos θ+1=√3 sin θ}. Then Σ_(θ∈ S)θ is equal to : Let S={θ ∈(0,2 π): 7 cos ² θ-3 sin ² θ-2 cos ² 2 θ=2}. Then, the sum of roots of all the… Let S={x ∈(-π/2, π/2): 9^(1-tan ² x)+9^(tan ² x)=10} and β=Σx ∈ S tan ²(x/3), then… More Mathematics chapters Frequently asked questions How many Trigonometric Equations questions are there for JEE Main? PrepWiser has 51 Trigonometric Equations questions for JEE Main, grouped into 2 topics such as General Solutions and Equations Reducible to Quadratic.
Are these Trigonometric Equations questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Trigonometric Equations questions? Open any Trigonometric Equations question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.