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Find the exact value of the expression whenever it is defined?

tan(arctan 6/5 + arccos 7/25)

Answer 1

Violet Anderson

#-162/109# or #-78/179#

We use the formula

#tan(A+B) = (tanA+tanB)/(1-tanAtanB)#

In this problem

#A = tan^-1(6/5) implies tanA = 6/5#

and

#B = cos^-1(7/25) implies sec B = 25/7 implies#

#tan^2 B = sec^2B-1 = (25/7)^2-1=576/49 implies #

#tan^2B = (24/7)^2#

So, #tanB = +24/7# or #tan B = -24/7#

If #tan B = +24/7#, we have

#tan(A+B) = (6/5+24/7)/(1-6/5 times 24/7) = (6 times 7+24 times 5)/(5 times 7-6times 24) = -162/109#

On the other hand, if #tan B = -24/7#, we have

#tan(A+B) = (6/5-24/7)/(1-6/5 times (-24/7)) = (6 times 7-24 times 5)/(5 times 7+6times 24) = -78/179#

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Answer 2

Jordan Armstrong

Of course, please provide the expression you would like me to evaluate, and I'll help you find its exact value if it's defined.

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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.