If A+B+C=180, then tan left(frac{A+B}{2}right)= ...........

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8. Introduction to Trigonometry

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If $A+B+C=180,$ then $\tan \left(\frac{A+B}{2}\right)=$ ...........

A

$\cot \left(\frac{A+B}{2}\right)$

B

$\cot \frac{ C }{2}$

C

$\sec \frac{ C }{2}$

D

$\sin \frac{A}{2}$

Solution

$A+B+C=180 \quad \therefore A+B=180-C \quad \therefore \frac{A+B}{2}=90-\frac{C}{2}$

$\therefore \tan \left(\frac{A+B}{2}\right)=\tan \left(90-\frac{C}{2}\right)=\cot \frac{C}{2}$

Standard 10

Mathematics

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