Question

Evaluate cos(cos−1(−√32)+π6)

Answer 1

Answer:

- 1

Step-by-step explanation:

cos(cos⁻¹(−√3/2)+π/6)

First calculate value of cos⁻¹(−√3/2).

Let Cos⁻¹(−√3/2) = y

=> Cosy = −√3/2

Cos function is negative in 2nd and 3rd quadrant

=> −√3/2 = Cos(π - π/6) or Cos(π + π/6).

But since the principal range of Cos⁻¹ x is [0,π], Cos(π + π/6)  can be ruled out. Thus −√3/2 = Cos(π - π/6) = Cos 5π/6

=> Cosy = Cos 5π/6

=> y =  5π/6.

Thus Cos(cos⁻¹(−√3/2)+π/6)

= Cos(5π/6 + π/6)

= Cos (6π/6)

= Cos π

= - 1.