Trigonometric Ratios & Identities: JEE Questions & Solutions

The value of cosec 10^° - √3 sec 10^° is equal to:

If (cos² 48^° - sin² 12^°)/(sin² 24^° - sin² 6^°) = (α + β√5)/2, where α, β ∈ ℕ, then the value of α + β is.

Let α and β respectively be the maximum and the minimum values of the function f(θ) = 4(sin⁴(7π/2 - θ) + sin⁴(11π + θ)) - 2(sin⁶(3π/2 - θ)…

The sum of all the real solutions of the equation log_(x+3)(6x² + 28x + 30) = 5 - 2log_(6x+10)(x² + 6x + 9) is equal to

The least value of (cos² θ - 6sin θ cos θ + 3sin² θ + 2) is

Let π/2 < θ < π and cot θ = -1/2√2. Then the value of sin(15θ/2)(cos 8θ + sin 8θ) + cos(15θ/2)(cos 8θ - sin 8θ) is equal to

The value of (√3cosec 20^° - sec 20^°)/(cos 20^° cos 40^° cos 60^° cos 80^°) 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 13x/2-sin 13x/2) is equal to

If tan(A-B)/(tan A)+(sin² C)/(sin² A)=1, A,B,C∈(0,π/2), then:

The sum of all the elements in the range of f(x)=sgn(sin x)+sgn(cos x) +sgn(tan x)+sgn(cot x), where x≠ nπ/2, n∈ℤ, sgn(t)= 1, t>0 -1, t<0…

The value of (sin 70^°)(cot 10^° cot 70^° - 1) is:

The value of Σ_(r=1)¹³ 1/sin(π/4 + (r-1)π/6)sin(π/4 + rπ/6) = a√3 + b, where a, b ∈ ℤ. Then a² + b² is equal to:

Let M and m respectively be the maximum and the minimum values of f(x) = 1 + sin² x cos² x 4sin 4x sin² x 1 + cos² x 4sin 4x sin² x cos² x…

If sin x + sin² x = 1, x ∈ (0, π/2), then the expression (cos¹² x + tan¹² x) + 3(cos¹⁰ x + tan¹⁰ x + cos⁸ x + tan⁸ x) + (cos⁶ x + tan⁶ x)…

If 10 sin⁴ θ + 15 cos⁴ θ = 6, then the value of (27 csc⁶ θ + 8 sec⁶ θ)/(16 sec⁸ θ) is:

Let the set of all a in ℝ such that the equation cos(2x) + a sin(x) = 2a - 7 has a solution be [p, q], and r = tan(9^°) - tan(27^°) -…

The sum of the solutions x ∈ ℝ of the equation (3 cos(2x) + cos³(2x))/(cos⁶(x) - sin⁶(x)) = x³ - x² + 6 is:

The number of solutions of the equation 4 sin² x - 4 cos³ x + 9 - 4 cos x = 0, for x ∈ [-2π, 2π], is:

The value of tan 9^° - tan 27^° - tan 63^° + tan 81^° is:

Let f(x) = (sin x + cos x - √2)/(sin x - cos x), where x ∈ [0, π] - {π/4}. Then f(7π/12) · f''(7π/12) is equal to: