Question

How do you evaluate `sec(cot^-1(-2))` without a calculator?

Answer 1

`sqrt 5/2`

Explanation:

Let `a = cot^(-1)(-2) in Q4`

Then, tan a=-1/2. cos will be positive and so is its reciprocal secant in

Q4.

The given expression is

`sec a = sqrt(1+tan^2a)=sqrt(1=(-1/2)^2)=sqrt 5/2`

If a is assumed to be in Q2, instead, the answer will be `-sqrt 5/2`.