Trigonometric Equations: JEE Questions & Solutions

Let cos(α + β) = -1/10 and sin(α - β) = 3/8, where 0 < α < π/3 and 0 < β < π/4. If tan 2α = 3(1 - r√5)/√11(s + √5), r, s ∈ ℕ, then the…

Number of solutions of √3 cos 2θ + 8 cos θ + 3√3 = 0, θ ∈ [-3π, 2π] is:

The number of elements in the set {x∈[0,180^°]: tan(x+100^°)=tan(x+50^°)tan xtan(x-50^°)} is

The sum of all values of θ ∈ [0, 2π] satisfying 2sin²θ = cos 2θ and 2cos²θ = 3sinθ is:

If θ ∈ [-2π, 2π], then the number of solutions of 2√2 cos²θ + (2 - √6) cosθ - √3 = 0 is:

If θ ∈ [-7π/6, 4π/3], then the number of solutions of √3csc²θ - 2(√3 - 1)cscθ - 4 = 0, is equal to:

The number of solutions of the equation 2x + 3tan x = π, x ∈ [-2π, 2π] - { ± π/2, ± 3π/2 } is

The number of solutions of the equation (4 - √3) sin x - 2√3 cos² x = (-4)/(1 + √3), x ∈ [-2π, 5π/2] is

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 y + γ = 0, then α² + β² + γ² is equal…

The number of solutions of the equation cos 2θ cos ( θ/2) + cos ( 5θ/2) = 2 cos³ ( 5θ/2) in the interval [ -π/2, π/2 ] is:

Let A = { θ ∈ [0, 2π]: 1 + 10 Re( (2 cos θ + i sin θ)/(cos θ - 3i sin θ)) = 0 }. Then Σ_(θ ∈ A) θ² is equal to:

If 2tan²(θ) - 5sec(θ) = 1 has exactly 7 solutions in the interval [0, nπ/2] for the least value of n ∈ ℕ, then Σ_(k=1)ⁿ k/2^k is equal to:

If α, with -π/2 < α < π/2, is the solution of 4cos(θ) + 5sin(θ) = 1, then the value of tan(α) is:

If 2sin³ x + sin 2x cos x + 4sin x - 4 = 0 has exactly 3 solutions in the interval [0, nπ/2], n ∈ ℕ, then the roots of the equation x² + nx…

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 A + B is equal to:

If m and n respectively are the numbers of positive and negative values of θ in the interval [-π, π] that satisfy the equation cos 2θ ·…

Let f(θ) = 3(sin⁴(3π/2 - θ) + sin⁴(3π + θ)) - 2(1 - sin²(2θ)), and S = {θ ∈ [0, π]: f'(θ) = -√3/2}. If 4β = Σ_(θ ∈ S) θ, then f(β) is equal…

The set of all values of λ for which the equation cos² (2x) - 2sin⁴ x - 2cos² x = λ has a solution is:

96 cos(π/33) cos(2π/33) cos(4π/33) cos(8π/33) cos(16π/33) is equal to:

Let S = { x ∈ ( -π/2, π/2): 9^(1 - tan² x) + 9^(tan² x) = 10 } and β = Σ_(x ∈ S) tan² ( x/3), then 1/6( β - 14)² is equal to:

The number of elements in the set S = { θ ∈ [0, 2π]: 3 cos⁴ θ - 5 cos² θ - 2 sin⁶ θ + 2 = 0 } is:

For x ∈ (-1, 1], the number of solutions of the equation sin⁻¹x = 2tan⁻¹x is equal to.