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Find the principal values of each of the following:
Let us assume 2tan = θ
We know tan = –1
∴ 2tan = 2(–1)
⇒ 2tan = –2
∴ The question converts to sec–1(–2)
Now,
Let sec–1(–2) = y
⇒ sec y = –2
= – sec = 2
= sec
= sec
The range of principal value of sec–1is [0, π]–{}
and sec = –2
∴ The principal value of sec–1(2tan) is