PrepWiser › Learn › Mathematics › Trigonometric Ratios & IdentitiesTrigonometric Ratios & Identities — JEE Main PYQs & Practice Questions Trigonometric Ratios & Identities is a Mathematics chapter in the JEE Main syllabus. This page brings together 72 previous-year and practice questions on Trigonometric Ratios & Identities, organised into 7 topics: Trigonometric Ratios and Signs, Allied Angle Formulas, Compound Angle Formulas, Multiple and Sub-Multiple Angles, Product-to-Sum and Sum-to-Product, Maximum and Minimum Values and Heights and Distances. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Trigonometric Ratios and Signs If 10 sin⁴ θ+15 cos⁴ θ=6, then the value of (27cosec⁶θ+8 sec⁶ θ)/(16 sec⁸ θ) is If for x ∈ (0,π/2), log₁₀sinx + log₁₀cosx = -1 and log₁₀(sinx + cosx) = 1/2(log₁₀ n -… sin θ ≤ 1 for all real θ. If sin x=-3/5, where π<x<3π/2, then 80(tan² x-cos x) is equal to tan 45° = x. The value of tan 9°-tan 27°-tan 63°+tan 81° is __________. α=sin 36° is a root of which of the following equation? If 15sin⁴α + 10cos⁴α = 6, for some α ∈R, then the value of 27sec⁶α + 8cosec⁶α is equal… The value of cot π/24 is : If the value of (3 cos 36°+5 sin 18°)/(5 cos 36°-3 sin 18°) is (a√5-b)/c, where a,b,c… The value of cosec10°-√3 sec 10° is equal to : The value of (sin 70°)(cot 10°cot 70°-1) is If cos x = 1/2 and x is in [0, 2π], then x = The value of 2sin (12°) - sin (72°) is : The number of solutions, of the equation eˢⁱⁿˣ-2e⁻ˢⁱⁿˣ=2, is : If tan 15°+1/(tan 75°)+1/(tan 105°)+tan 195°=2a, then the value of (a+1/a) is : If sin θ = 3/5, then cos θ = The value of 36(4 cos² 9°-1)(4 cos² 27°-1)(4 cos² 81°-1)(4 cos² 243°-1) is : If sin x+sin² x=1, x∈ (0,π/2), then (cos¹² x+tan¹² x)+3(cos¹⁰ x+tan¹⁰ x+cos⁸ x+tan⁸… Allied Angle Formulas Compound Angle Formulas Let tan A,tan B, where A,B∈ (-π/2,π/2), be the roots of the quadratic equation… If 0 < x, y < π and cosx + cosy - cos(x + y) = 3/2, then sinx + cosy is equal to : If tan (π/9),x,tan (7π/18) are in arithmetic progression and tan (π/9),y,tan (5π/18) are… The value of sin 60° cos 30° + cos 60° sin 30° is: If cotα = 1 and secβ = -5/3, where π<α<3π/2 and π/2<β<π, then the value of tan (α+β) and… If (tan (A-B))/(tan A)+(sin² C)/(sin² A)=1, A, B,C∈ (0,π/2), then For α,β∈ (0,π/2), let 3 sin (α+β)=2 sin (α-β) and a real number k be such that tan α=k… If for θ∈ [-π/3,0], the points (x,y)=(3 tan (θ+π/3),2 tan (θ+π/6)) lie on xy+α x+β… If tan A=1/√x(x²+x+1),tan B=√x/√(x²+x+1) and tan C=(x⁻³+x⁻²+x⁻¹)^(1/2),0<A,B,C<π/2, then… Multiple and Sub-Multiple Angles Let cos (α+β)=-1/10 and sin (α-β)=3/8, where 0<α<π/3 and 0<β<π/4. If tan… Let P={θ∈ [0,4π]:tan² θ≠ 1} and S={a∈ ℤ:2(cos⁸ θ-sin⁸ θ)sec 2θ=a²,θ∈ P}. Then n(S) is: If (√2 sin α)/√(1+cos 2α)=1/7 and √((1-cos 2β)/2)=1/√10 α,β∈ (0,π/2) then tan(α + 2β) is… Consider the function f:[1/2, 1] → ℝ defined by f(x)=4 √2 x³-3 √2 x-1. Consider the… If sin (π/18)sin (5π/18)sin (7π/18)=K, then the value of sin (10Kπ/3) is: Let the set of all a∈ R such that the equation cos 2x+a sin x=2a-7 has a solution be… cosec18° is a root of the equation : If L = sin²(π/16) - sin²(π/8) and M = cos²(π/16) - sin²(π/8), then : Let f(θ)=3(sin⁴(3π/2-θ)+sin⁴(3π+θ))-2(1-sin²2θ) and S={θ∈ [0,π]:f'(θ)=-√3/2}. If… If sin θ+cos θ=1/2, then 16(sin(2θ) + cos(4θ) + sin(6θ)) is equal to : If cot x=5/12 for some x∈ (π,3π/2), then sin 7x(cos 13x/2+sin 13x/2)+cos 7x(cos… The value of cos³(π/8) cos(3π/8)+sin³(π/8) sin(3π/8) is : Let π/2<θ<π and cot θ=-1/2√2. Then the value of sin (15θ/2)(cos 8θ+sin 8θ)+cos… If the equation cos⁴ θ + sin⁴ θ + λ = 0 has real solutions for θ, then λ lies in the… The value of (√3cosec20°-sec 20°)/(cos 20°cos 40°cos 60°cos 80°) is equal to Product-to-Sum and Sum-to-Product The value of cos (2π/7)+cos (4π/7)+cos (6π/7) is equal to : 16 sin (20°)sin (40°)sin (80°) is equal to : Suppose θ∈ [0,π/4] is a solution of 4 cos θ-3 sin θ=1. Then cos θ is equal to : If e^((cos²x+cos⁴x+cos⁶x+...∞)logₑ2) satisfies the equation t² - 9t + 8 = 0, then the… 2 sin (π/22)sin (3π/22)sin (5π/22)sin (7π/22)sin (9π/22) is equal to : If sin²(10°)sin (20°)sin (40°)sin (50°)sin (70°)=α-1/16 sin (10°), then 16+α⁻¹ is equal… If (cos ² 48°-sin ² 12°)/(sin ² 24°-sin ² 6°)=(α+β √5)/2 , where α, β ∈ ℕ , then α+β is… If x=Σₙ₌₀^∞(-1)ⁿtan²ⁿθ and y=Σₙ₌₀^∞cos²ⁿθ for 0 < θ < π/4, then : 96 cos π/33 cos 2π/33 cos 4π/33 cos 8π/33 cos 16π/33 is equal to : If A=(sin 3°)/(cos 9°)+(sin 9°)/(cos 27°)+(sin 27°)/(cos 81°) and B=tan 81°-tan 3°, then… If Σᵣ₌₁¹³{1/(sin (π/4+(r-1)π/6)sin (π/4+rπ/6))}=a√3+b,a,b∈ Z, then a²+b² is equal to : Let aₖ⃗=(tan θₖ)î+ĵ and bₖ⃗=î-(cot θₖ)ĵ, where θₖ=2ᵏ⁻¹π/(2ⁿ+1), for some n∈ ℕ,n>5. Then… Maximum and Minimum Values Let α and β respectively be the maximum and the minimum values of the function… The range of the function, f(x) = log _(√5)( 3 + cos ( 3π/4 + x ) + cos ( π/4 + x ) +… The set of all values of λ for which the equation cos²2x-2sin⁴x-2cos²x=λ has a real… The minimum value of 2ˢⁱⁿˣ + 2ᶜᵒˢˣ is : Let |cos θ cos (60-θ) cos (60+θ)| ≤ 1/8, θ ε[0,2 π]. Then, the sum of all θ ∈[0,2 π]… Let the range of the function f(x)=6+16 cos x· cos (π/3-x)· cos (π/3+x)· sin 3x· cos… Let α = max _(x ∈ R) { 8²ˢⁱⁿ³ˣ.4⁴ᶜᵒˢ³ˣ} and β = min _(x ∈ R) { 8²ˢⁱⁿ³ˣ.4⁴ᶜᵒˢ³ˣ}. If 8x²… The least value of (cos² θ-6 sin θ cos θ+3 sin² θ+2) is If the range of f(θ)=(sin ⁴ θ+3 cos ² θ)/(sin ⁴ θ+cos ² θ), θ ∈ ℝ is [α, β], then the… The number of integral values of 'k' for which the equation 3 sin x+4 cos x=k+1 has a… Let the range of the function f(x)=1/(2+sin 3 x+cos 3 x), x ∈ ℝ be [a, b]. If α and β ar… The number of elements in the set S={x ∈ ℝ: 2 cos ((x²+x)/6)=4ˣ+4⁻ˣ} is : Heights and Distances More Mathematics chapters Frequently asked questions How many Trigonometric Ratios & Identities questions are there for JEE Main? PrepWiser has 72 Trigonometric Ratios & Identities questions for JEE Main, grouped into 7 topics such as Trigonometric Ratios and Signs, Allied Angle Formulas and Compound Angle Formulas.
Are these Trigonometric Ratios & Identities 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 Ratios & Identities questions? Open any Trigonometric Ratios & Identities question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.