Use a sum or difference formula to find the exact value of the following (tanfrac (3pi )/(4)+tan(pi )/(12))(1-tan(3pi )/(4)tan(pi )/(12)) square

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Answer 1

To find the exact value of the given expression, we can use the tangent sum formula:

In this case, we have

and

.First, let's find the values of

and

.

To find

, we can use the tangent subtraction formula:

Let

and

, then

.

Since

and

, we have:

Now, substitute the values of

and

into the original expression:

Simplify the numerator and denominator separately:Numerator:

Denominator:

Now, divide the numerator by the denominator:

Therefore, the exact value of the given expression is

.

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