For the following trigonometric expression, evaluate and give the answer as an exact value in radians.

tan^{- 1}(- 1)

Identify the equation which has a solution equal to $\frac{2\pi}{3}$ .

Determine the exact value of the given inverse trigonometric function without using a calculator.

$y=\sec^{-1}\left(-1\right)+\sec^{-1}\left(2\right)$

Determine the exact value of the expression without using a calculator.

$\cos\left(2\arctan\frac{84}{13}\right)$

Apply the most suitable technique to determine the solution of the following equation within the interval [0, 2π), employing exact values whenever feasible or providing approximations accurate to four significant figures.

2 cos A - 19 = 5 cos A + 11

For the following trigonometric equation, perform substitution to identify which of the following angles is a solution.

cos x = (√3)/2

a) π/6

b) π/3

c) π/4

d) π/2

Solve the following trigonometric equation on the interval [0, 2π) with the help of a calculator. Round your final answer up to four decimal places.

5sin² x - 3 = 0