Question

Find the value of tan⁻¹(1)+cos⁻¹(−1/2)+sin⁻¹(−1/2).

Answer 1

cos y=−1/2=−cosπ/3=cos(π−π/3)=cos(2π/3)

We know that the range of the principal value branch of cos⁻¹ is [0,].

∴cos⁻¹(−1/2)=2π/3

Let sin⁻¹(−1/2)=z, then

sin z=-1/2=sin− π/6=(−π/6)