Find the number of solutions of the equation - the minimum

Question

Trigonometry

1: The general value of θ satisfying both sinθ = -1/2 and tanθ = 1/√3 is :

(A) 2nΠ          (B) 2nΠ + 7Π/6
(C) nΠ + Π/4  (D) 2nΠ + Π/4

2: The number of solutions of the equation x³ + 2x² +5x + 2cosx = 0 in [0, 2Π] is:

(A) 0   (B) 1
(C) 2   (D) 3

3: Solve cot (sinx + 3) = 1.

(A) 2nΠ    (B) 2nΠ + 7Π/6

(C) nΠ + Π/4 (D) nΠ + (-1)ⁿ sin^-1(5Π/4 -3)

4: The minimum value of cos(cosx) is

(A) 0       (B) -1
(C) -cos1 (D) cos1

5: If 3sinθ + 5cosθ = 5, then the value of 5sinθ - 3cosθ is equal to
(A) 0      (B) 1
(C) 2      (D) 3