# Trigonometry

### Let a vertical tower AB have its end A on the level ground

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

### If 5(tan^2 x – cos^2x) = 2 cos 2x + 9, then the value of cos 4x is

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

### If 0 ≤ x the number of real values of x

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

### The sum of the radii of inscribed and circumscribed circles

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)

### Let cos(a + b) = 4/5 and let sin(a - b) = 5/13

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

### In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1

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

### If A = sin^2 x + cos^4 x, then for all real x

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

### Let fk(x) = 1/k(sin^k x + cos^k x) where x ∈ R and k ≥ 1

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

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

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

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

### The number of real values of x, which satisfy the equation cosx + cos2x + cos3x + cos4x = 0

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