Get the solution to "How to prove that sec⁡(π3)tan⁡(π3)=23?"

emnehefteye4

Answered question

2023-01-09

How to prove that

\sec (\frac{π}{3}) \tan (\frac{π}{3}) = 2 \sqrt{3}

Mikayla Cox

Beginner2023-01-10Added 15 answers

You can check the results by dividing your left side of the identity into its component trigonometric functions.
Remember that

\frac{π}{3} = 60 °

and this is a ""special"" angle which has ""known"" values of

\sin, \cos, \tan, \dots

etc.
Now:

\sec (\frac{π}{3}) = \frac{1}{\cos (\frac{π}{3})} = \frac{1}{\frac{1}{2}}

\tan (\frac{π}{3}) = \frac{\sin (\frac{π}{3})}{\cos (\frac{π}{3})} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}

Let's combine them all:

\sec (\frac{π}{3}) \tan (\frac{π}{3}) = \frac{1}{\frac{1}{2}} \cdot \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} =

manipulate your fractions to get:

= 4 \cdot \frac{\sqrt{3}}{2} = 2 \sqrt{3}

Which is indeed the result you needed to get to satisfy the identity.

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