How do you evaluate $cos [Sec ^-1 (-5)]$ ?

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Answer 1 · 2016-08-28T02:00:56

$-1/5$

As cosine is the reciprocal of secant,

$a = sec^(-1)(-5) = cos^(-1)(-1/5)$ ,

the given expression is

$cos a = -1/5$ .

Answer 2 · 2016-08-29T02:45:50

$cos(sec^-1(-5))=-1/5$

Let:

$x=cos(sec^-1(-5))$

We can then say that:

$cos^-1(x)=sec^-1(-5)$

Using the same principle to now isolate the $-5$ , we say that:

$sec(cos^-1(x))=-5$

Since $sec(x)=1/cos(x)$ , rewrite the left-hand side:

$1/cos(cos^-1(x))=-5$

$cos(x)$ and $cos^-1(x)$ undo one another, being inverse functions:

$1/x=-5$

Taking the reciprocal of both sides:

$x=-1/5$

Thus:

$cos(sec^-1(-5))=-1/5$

How do you evaluate cos [Sec ^-1 (-5)]cos [Sec ^-1 (-5)]?