Question

What is the principal value of cos -¹[cos 2pi/3] + sin-¹[cos 2pi/3]?

Answer 1

Given : cos -¹[cos 2pi/3] + sin-¹[cos 2pi/3]

To find : Principal Value

Step-by-step explanation:

cos -¹[cos 2pi/3] + sin-¹[cos 2pi/3]?

principal value of cos -¹ lies between [0 , π ]

principal value of Sin -¹ lies between [-π/2 , π/2]

cos -¹[cos 2π/3] + sin-¹[cos 2π/3]

= 2π/3  + sin-¹[Sin ( π/2 -2π/3)]

= 2π/3  + sin-¹[Sin ( -π/6)]

= 2π/3  + (-π/6)

=  2π/3 - π/6

= (4π - π)/6

= 3 π/6

= π/2

principal value of  cos -¹[cos 2π/3] + sin-¹[cos 2π/3] = π/2

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