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.

tan (sin⁻¹ 2x)

Determine the exact value of the following trigonometric expression by sketching.

tan (cos^-1 (12/37))

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

$\cos\left(\tan^{-1}\left(-5\right)\right)$