Inverse Trigonometric Functions

Find the principal values of the following: sin⁻¹(-1/2)

Find the principal values of the following: cos⁻¹($\sqrt{3}$/2)

Find the principal values of the following: cosec⁻¹(2)

Find the principal values of the following: tan⁻¹(-$\sqrt{3}$)

Find the principal values of the following: cos⁻¹(-1/2)

Find the principal values of the following: tan⁻¹(-1)

Find the principal values of the following: sec⁻¹(2/$\sqrt{3}$)

Find the principal values of the following: cot⁻¹($\sqrt{3}$)

Find the principal values of the following: cos⁻¹(-1/$\sqrt{2}$)

Find the principal values of the following: cosec⁻¹(-$\sqrt{2}$)

Find the values of the following: tan⁻¹(1) + cos⁻¹(-1/2) + sin⁻¹(-1/2)

Find the values of the following: cos⁻¹(1/2) + 2sin⁻¹(1/2)

If sin⁻¹x = y, then

tan⁻¹$\sqrt{3}$ - sec⁻¹(-2) is equal to

Prove the following:

Prove the following:

Write the following functions in the simplest form: tan⁻¹[($\sqrt{1+x²}$ - 1)/x], x $\neq$ 0

Write the following functions in the simplest form: tan⁻¹[(cos x - sin x)/(cos x + sin x)], -π/4 < x < 3π/4

Write the following functions in the simplest form: tan⁻¹[x/$\sqrt{a² - x²}$], |x| < a

Write the following functions in the simplest form: tan⁻¹[(3a²x - x³)/(a³ - 3ax²)], a > 0; -a/$\sqrt{3}$ < x < a/$\sqrt{3}$