Question

In: Math

The principal value of tan-1(tan 3π/5) is (a) 2π/5 (b) -2π/5 (c) 3π/5 (d) -3π/5

The principal value of tan-1(tan 3π/5) is _____________.

(a) 2π/5

(b) -2π/5

(c) 3π/5

(d) -3π/5

Expert Solution

Answer : (b) -2π/5

Explanation :

We have to find the principal valve of tan-1 (tan 3π/5).

This can be written as:

tan-1 (tan 3π/5) = tan-1 (tan[π – 2π/5])

= tan-1 (- tan 2π/5)

[ since tan(π – x) = -tan x ]

= –tan-1 (tan 2π/5)

= –2π/5

Therefore,

Principal value of tan-1(tan 3π/5) is -2π/5.

(b) –2π/5

Rakesh answered 2 years ago

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