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

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Answer 1 · 2016-08-11T07:43:20

$sqrt 5/2$

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 $-sqrt 5/2$ .

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