The area of a ABC is a 2- b - c 2 then tan A is equal toA- 4-3B- 3-4C- 8-15DD- None of these

The correct option is C Here =a^2 (b c)^2 ⇒ =(2s 2c)(2s 2b)=4(s b)(s c) ∴1 4 = (s b)(s c)/ = tan A/2 ⇒ tan A= 2tanA 2/1 tan^2A 2=2×1 4/1 (1 4)^2=8 15 ...

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Standard VII

Mathematics

Area of a Triangle

The area of a...

Question

The area of a $△$ ABC is $a^{2} - (b - c)^{2}$ then tan A is equal to

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None of these

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Solution

The correct option is C

Here $△ = a^{2} - (b - c)^{2}$
$\Rightarrow △ = (2 s - 2 c) (2 s - 2 b) = 4 (s - b) (s - c)$
$∴ \frac{1}{4} = \frac{(s - b) (s - c)}{△} = t a n \frac{A}{2}$
$\Rightarrow t a n A = \frac{2 t a n \frac{A}{2}}{1 - t a n^{2} \frac{A}{2}} = \frac{2 \times \frac{1}{4}}{1 - (\frac{1}{4})^{2}} = \frac{8}{15}$

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The area of a △ ABC is a2−(b−c)2 then tan A is equal to

The correct option is C Here △=a2−(b−c)2 ⇒△=(2s−2c)(2s−2b)=4(s−b)(s−c) ∴14=(s−b)(s−c)△=tanA2 ⇒tanA=2tanA21−tan2A2=2×141−(14)2=815

The area of a $△$ ABC is $a^{2} - (b - c)^{2}$ then tan A is equal to