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Solving: $\left(\sin\left(\frac{2}{3}\right)^{-1}- \cos\left(\frac{1}{3}\right)^{-1}\right)\tan\left(\right)$
Solve instead: $tan\left(sin^{-1}\left(\frac{2}{3}\right)-cos^{-1}\left(\frac{1}{3}\right)\right)$

Exercise

$tan\left(sin^{-1}\left(\frac{2}{3}\right)-cos^{-1}\left(\frac{1}{3}\right)\right)$

Step-by-step Solution

1

Multiply the single term $\tan\left(\right)$ by each term of the polynomial $\left(\sin\left(\frac{2}{3}\right)^{-1}- \cos\left(\frac{1}{3}\right)^{-1}\right)$

$\sin\left(\frac{2}{3}\right)^{-1}\tan\left(\right)- \cos\left(\frac{1}{3}\right)^{-1}\tan\left(\right)$

Final answer to the exercise

$\sin\left(\frac{2}{3}\right)^{-1}\tan\left(\right)- \cos\left(\frac{1}{3}\right)^{-1}\tan\left(\right)$

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$csc^2x-1$

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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