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How do you simplify #tan(cos^(-1)x)#?

Answer 1

Violet Anderson

Let #a=cos^(-1)x#. Then #x= cos a and tan a=sina/cos a=+-(sqrt(1-x^2)/x)# Answer:#+-(sqrt(1-x^2)/x)#

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Answer 2

Abigail Armstrong

To simplify ( \tan(\cos^{-1} x) ), you can use trigonometric identities. Let ( \theta = \cos^{-1} x ). Then, ( \cos \theta = x ). Using the Pythagorean identity, ( \sin^2 \theta + \cos^2 \theta = 1 ), we can find ( \sin \theta ). Finally, we use the definition of tangent to simplify.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.