Find the exact value of the expression. Do not use a calculator. StartStartFraction tangent StartFraction pi Over 3 EndFraction OverOver 2 EndEndFraction plus StartStartFraction 1 OverOver cosecant StartFraction pi Over 3 EndFraction EndEndFraction tangent pi/3 over 2 plus 1 over CSC pi/3
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Question:
Find the exact value of the expression. Do not use a calculator. StartStartFraction tangent StartFraction pi Over 3 EndFraction OverOver 2 EndEndFraction plus StartStartFraction 1 OverOver cosecant StartFraction pi Over 3 EndFraction EndEndFraction
tangent pi/3 over 2 plus 1 over CSC pi/3
tangent pi/3 over 2 plus 1 over CSC pi/3
Answers
Answer: √3Step-by-step explanation: [tex]\dfrac{1}{2}\tan{\dfrac{\pi}{3}}+\dfrac{1}{\csc{\dfrac{\pi}{3}}}=\dfrac{1}{2}\tan{\dfrac{\pi}{3}}+\sin{\dfrac{\pi}{3}}\\\\=\dfrac{1}{2}\sqrt{3}+\dfrac{\sqrt{3}}{2}=\boxed{\sqrt{3}}[/tex]
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