In Exercises 39–54, find the exact value of each expression, if p...

Question

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator.

tan (tan⁻¹ 125)

Accepted Answer

Hello, today we're gonna be determining the exact value of the following trigonometric expression. So what we are given is tangent of tangent inverse of 175. Now there is one property of trigonometric functions that is going to help us solve this problem whenever we multiply a trigonometric function to its respective inverse or we multiply an inverse of a trigonometric function to its respective function. What ends up happening is that the product of the function and its inverse is going to cancel each other out. And what we are left with is just the inside angle. Now, this property is true for all six of the trigonometric functions. And if we utilize this property on the expression tangent multiplied by tangent inverse is going to cancel out the trigonometric expressions leaving us with the inside angle which is 175. And this is going to be the exact value of the given trigonometric expression. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. tan (tan⁻¹ 125)