In a ABC - a - b - c tan A -2-tan B -2 isA- 2 ccotc-2B- tanC-2C- 2 bcot B-2D- 2 a A-2

The correct option is A (a+b+c)(tanA 2+tanB 2) =2s(tanA 2+tanB 2) =2s(/s(s a)+/s(s b))=2(/(s a)+/(s b)) =2(s b+s a/(s a)(s b))=2(c/(s a)(s b)) =2c cotC 2 ...

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Byju's Answer

Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

In a ABC , a ...

Question

In a $△ A B C, (a + b + c) (t a n \frac{A}{2} + t a n \frac{B}{2})$ is

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Solution

The correct option is A

$(a + b + c) (t a n \frac{A}{2} + t a n \frac{B}{2})$
= $2 s (t a n \frac{A}{2} + t a n \frac{B}{2})$
= $2 s (\frac{△}{s (s - a)} + \frac{△}{s (s - b)}) = 2 (\frac{△}{(s - a)} + \frac{△}{(s - b)})$
= $2 △ (\frac{s - b + s - a}{(s - a) (s - b)}) = 2 △ (\frac{c}{(s - a) (s - b)})$
= $2 c c o t \frac{C}{2}$

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In a △ABC,(a+b+c)(tanA2+tanB2) is

The correct option is A (a+b+c)(tanA2+tanB2) =2s(tanA2+tanB2) =2s(△s(s−a)+△s(s−b))=2(△(s−a)+△(s−b)) =2△(s−b+s−a(s−a)(s−b))=2△(c(s−a)(s−b)) =2c cotC2

In a $△ A B C, (a + b + c) (t a n \frac{A}{2} + t a n \frac{B}{2})$ is