# What is #cos[sin^(-1)(-1/2 ) + cos^(-1)(5/13) ]#?

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By the sum angle formula that's

These questions are confusing enough with the funky inverse function notation. The real problem with questions like this is it's generally best to treat the inverse functions as multivalued, which may mean the expression has multiple values as well.

Anyway, this is the cosine of the sum of two angles, and that means we employ the sum angle formula:

Cosine of inverse cosine and sine of inverse sine are easy. The cosine of inverse sine and sine of inverse cosine are also straightforward, but there's where the multivalued issue comes in.

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To find the value of ( \cos[\sin^{-1}(-1/2) + \cos^{-1}(5/13)] ):

- Start by finding the values of ( \sin^{-1}(-1/2) ) and ( \cos^{-1}(5/13) ).
- Once you have those values, add them together.
- Then, take the cosine of the result obtained in step 2.

This process will give you the value of ( \cos[\sin^{-1}(-1/2) + \cos^{-1}(5/13)] ).

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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.

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.

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.

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