Question

tan^-1 + cos^-1(-1/2) + sin^-1(-1/2)

Answer 1

Answer:

3π/4

Step-by-step explanation:

Tan⁻¹ (1)  + Cos⁻¹ (-1/2) + Sin⁻¹(-1/2)

We know that tan 45 = 1 , Cos 60 = 1/2 and Sin 30 = 1/2

So,

Tan⁻¹ (1) = 45° = π/4. (Since range of principal value of Tan⁻¹ is [-π/2, π/2]

Cos⁻¹ (-1/2) = - 60° = - π/3 = π - π/3 = 2π/3. (Since range of principal value

                                                                           of Cos⁻¹ is [0,π]

Sin⁻¹(-1/2) = - 30° = - π/6 ((Since range of principal value of Sin⁻¹ is [-π/2,  

                                               π/2]

Thus the question becomes

π/4 + 2π/3 - π/6

= 3π + 8π - 2π / 12

=  9π/12 = 3π/4