1
If 5tanθ = 4, then (5sinθ -3cosθ)/(5sinθ +2cosθ) is equal to ...
Trigonometric Ratios and Identities
2
If 2sec2θ = tan φ + cot φ, then one of the values of θ + φ is ...
Trigonometric Ratios and Identities
3
If sin x + cosec x = 2, then sinⁿ x + cosecⁿ x is equal to ...
Trigonometric Ratios and Identities
4
A quadratic equation whose roots are cosec²θ and sec²θ can be ...
Trigonometric Ratios and Identities
5
If π< a < 3π/2, then (1 - cos a / 1 + cos a)^.5 + (1 + cos a / 1 - c ...
Trigonometric Ratios and Identities
6
The value of cos(π/7) + cos(2π/7) + cos(3π/7) + cos(4π/7) + cos(5π/7) ...
Trigonometric Ratios and Identities
7
The least value of 2sin²θ + 3cos²θ is ...
Trigonometric Ratios and Identities
8
The greatest value of sin⁴θ + cos⁴θ is ...
Trigonometric Ratios and Identities
9
If f(x) = cos²θ + sec²θ, then ...
Trigonometric Ratios and Identities
10
If f(x) = sin⁶x + cos⁶x, then the range of f(x) is ...
Trigonometric Ratios and Identities
11
If a ≤ 3cosx + 5sin(x - π/6) ≤ b for all x, then (a, b) is ...
Trigonometric Ratios and Identities
12
The equation sinx(sinx + cosx) = k has real solutions if and only if k ...
Trigonometric Ratios and Identities
13
If cot(α + β) = 0, then sin(α + 2β) can be ...
Trigonometric Ratios and Identities
14
sin²ⁿx + cos²ⁿx lies between ...
Trigonometric Ratios and Identities
15
The roots of the equation 4x² - 2√5x + 1 = 0 are ...
Trigonometric Ratios and Identities
16
If 3π/4 < α < π, then (2cotα +cosecsq α)^.5 is equal to ...
Trigonometric Ratios and Identities
17
If f(θ) = 5 cos θ + 3 cos (θ + π/3) + 3, then range of f(θ) is ...
Trigonometric Ratios and Identities
18
If α, β, γ, δ are the smallest positive angles in ascending order of m ...
Trigonometric Ratios and Identities
19
Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra ...
Trigonometric Ratios and Identities
20
If sinθ1 + sinθ2 + sinθ3 = 3, then cosθ1 + cosθ2 + cosθ3 is equal to ...
Trigonometric Ratios and Identities
21
If sin²θ = (x² + y² + 1) / (2x), then x must be ...
Trigonometric Ratios and Identities
22
If sin(α + β) = 1 and sin(α - β) = 1/2, then tan(α + 2β) tan(2α + β) i ...
Trigonometric Ratios and Identities
23
If cosecθ - cotθ = q, then the value of cosecθ is ...
Trigonometric Ratios and Identities
24
If sinθ + cosθ = 1/5 and 0 ≤ θ < π, then tanθ is ...
Trigonometric Ratios and Identities
25
If x = 2sinθ / (1 + cosθ + sinθ), then 1 - cosθ + sinθ / (1 + sinθ) is ...
Trigonometric Ratios and Identities
26
If θ = π / 4n, then the value of tanθ tan2θ ... tan(2n - 2)θ tan(2n - ...
Trigonometric Ratios and Identities
27
The value of the expression 2(sin1° + sin2° + ... + sin89°) / 2(cos1° ...
Trigonometric Ratios and Identities
28
If secα and cosecα are the roots of x² - px + q = 0, then ...
Trigonometric Ratios and Identities
29
If a + b = 3 - cos 4θ and a - b = 4 sin 2θ, then ab is always less tha ...
Trigonometric Ratios and Identities
30
The value of cos²10° - cos10° cos50° + cos²50° is equal to ...
Trigonometric Ratios and Identities
31
The numerical value of tan 20° tan 80° cot 50° is equal to ...
Trigonometric Ratios and Identities
32
If tan²θ = 2 tan²φ + 1, then cos²θ + sin²φ equals ...
Trigonometric Ratios and Identities
33
The value of cot 70° + 4 cos 70° is ...
Trigonometric Ratios and Identities
34
If x1 and x2 are two distinct roots of the equation a cos x + b sin x ...
Trigonometric Ratios and Identities
35
If tan α is equal to the integral solution of the inequality 4x² - 16x ...
Trigonometric Ratios and Identities
36
If cos(x - y) cos(z + t) + cos(x + y) cos(z - t) = 0, then the value o ...
Trigonometric Ratios and Identities
37
Let f(n) = 2 cos nx ∀ n ∈ N, then f(1)f(n + 1) - f(n) is equal to ...
Trigonometric Ratios and Identities
38
If in triangle ABC, sin A cos B = √3/4 and 3 tan A = tan B, then the t ...
Trigonometric Ratios and Identities
39
If A and B are acute positive angles satisfying the equations 3 sin² A ...
Trigonometric Ratios and Identities
40
Let f(θ) = cot(θ)/1+coθ and α + β = 5π/4, then the value f(α) f(β) is ...
Trigonometric Ratios and Identities
41
If y = (1 + tan A)(1 - tan B) where A - B = π/4, then (y + 1)^(y + 1) ...
Trigonometric Ratios and Identities
42
If sin(y + z - x), sin(z + x - y), sin(x + y - z) are in A.P., then ta ...
Trigonometric Ratios and Identities
43
If cos α + cos β = 0 = sin α + sin β, then cos 2α + cos 2β is equal to ...
Trigonometric Ratios and Identities
