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Exercise

$1+tan\left(\frac{3\pi}{4}\right)tan\left(\frac{5\pi}{12}\right)$

Step-by-step Solution

1

Apply the trigonometric identity: $\tan\left(\frac{\theta }{4}\right)$$=\frac{\sin\left(\frac{\theta }{2}\right)}{\cos\left(\frac{\theta }{2}\right)+1}$, where $x=3\pi $

$1+\frac{\sin\left(\frac{3\pi }{2}\right)}{\cos\left(\frac{3\pi }{2}\right)+1}\tan\left(\frac{5\pi }{12}\right)$

Final answer to the exercise

$1+\frac{\sin\left(\frac{3\pi }{2}\right)}{\cos\left(\frac{3\pi }{2}\right)+1}\tan\left(\frac{5\pi }{12}\right)$

Try other ways to solve this exercise

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Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

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