Trigonometry

1

Let a vertical tower AB have its end A on the level ground. Let C be the midpoint of AB and P be a point on the ground such that AP = 2AB. If ∠BPC = β, then tan β is equal to:

  1. 6/7
  2. 1/4
  3. 2/9
  4. 4/9
2

If 5(tan2 x – cos2x) = 2 cos 2x + 9, then the value of cos 4x is

  1. -3/5
  2. 1/3
  3. 2/9
  4. -7/9
3

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation 

cos x + cos 2x + cos 3x + cos 4x = 0 is

  1. 3
  2. 5
  3. 7
  4. 9
4

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is

  1. a/2 cot(π/2n)
  2. a/4 cot(π/2n)
  3. a cot(π/n)
  4. a cot(π/2n)
5

Let cos(a + b) = 4/5 and let sin(a - b) = 5/13 where 0 ≤ a,b ≤ π/4. Then tan 2a is

  1. 20/17
  2. 25/16
  3. 56/33
  4. 19/12
6

In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to

  1. π/4
  2. 3π/4
  3. 5π/6
  4. π/6
7

If A = sin2 x + cos4 x, then for all real x

  1. 3/4 ≤ A ≤ 1
  2. 1 ≤ A ≤ 2
  3. 3/4 ≤ A ≤ 13/16
  4. 13/16 ≤ A ≤ 1
8

Let fk(x) = 1/k(sink x + cosk x) where x ∈ R and k ≥ 1. Then f4(x) - f6(x) equals

  1. 1/12
  2. 1/6
  3. 1/4
  4. 1/3
9

The number of solution of tan x + sec x = 2 cos x in [0, 2π) is

  1. 0
  2. 1
  3. 2
  4. 3
10

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation
cosx + cos2x + cos3x + cos4x = 0 is:

  1. 5
  2. 7
  3. 9
  4. 3