Determine the exact value of the following trigonometric expression without the help of the calculator.

tan (tan^-1 175)

Transform the following expression into an algebraic expression. Use a right triangle in writing the algebraic expression. Assume that the inverse trigonometric function is defined for its argument and assume that x > 0.

sin (cos⁻¹ (5/x))

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

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

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

cos^{- 1}((√2)/2)

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

cot^{- 1}(1)

Without using a calculator, determine the exact value of the expression:

sec⁻¹ (1)

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

tan 2x = - 1

a) 5π/8

b) 3π/8

c) 7π/12

d) 11π/12

For the following trigonometric equation, solve in the interval [0, 2π] and give the answer in exact radian measure.

9 csc x (4 sin x - 4) = 0

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.

10 cos x + 5√2 sin 2x = 0