Question

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What is the exact value of cos(tan−1(−1))/sin(cos−1(−3√2))?

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cos(tan−1(−1))/sin(cos−1(−3√2))=

Answer 1

The exact value of $\dfrac{cos(tan^{-1}(-1))}{sin(cos^{-1}(-\frac{3}{\sqrt{2}})}$ would be root 2.

What is a function?

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

$\dfrac{cos(tan^{-1}(-1))}{sin(cos^{-1}(-\frac{3}{\sqrt{2}})}$

We know that

The inverse tan(-1) = -π/4

cos(-π/4) = 1/√2

The inverse cos(√3/2) = π//6

sin(π/6) = 1/2

Then substitute

$\dfrac{cos(tan^{-1}(-1))}{sin(cos^{-1}(-\frac{3}{\sqrt{2}})}$

$\dfrac{(1/\sqrt{2}) }{(1/2)} \\\\= \sqrt{2}$

Learn more about function here:

https://brainly.com/question/2253924

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