In a ABC- if tan A -2-5-6 and tan B -2-20-37- thenA- 2 a - b - cB- a-b-c C- 2 c - a - bD- None of these

The correct option is B a gt;b gt;c tanA 2 tanB 2 or A 2B 2 or A B tan(A+B/2) = 5 6+20 37/1 5 6×20 37=305 122 Or tanC 2=122 305, As 20 37122 305 we Ge ...

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Standard XII

Mathematics

Conditional Identities

In a ABC, if ...

Question

In a $△ A B C$ , if $t a n \frac{A}{2} = \frac{5}{6} a n d t a n \frac{B}{2} = \frac{20}{37}$ ,then

2a = b+c

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a>b>c

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2c = a+b

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None of these

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Solution

The correct option is B
a>b>c

$t a n \frac{A}{2} > t a n \frac{B}{2} o r \frac{A}{2} > \frac{B}{2} o r A > B$
$t a n (\frac{A + B}{2}) = \frac{\frac{5}{6} + \frac{20}{37}}{1 - \frac{5}{6} \times \frac{20}{37}} = \frac{305}{122}$
Or $t a n \frac{C}{2} = \frac{122}{305}$ , As $\frac{20}{37} > \frac{122}{305}$ we
Get $t a n \frac{B}{2} > t a n \frac{C}{2} \Rightarrow B > C ∴ A > B > C \Rightarrow a > b > c$

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Similar questions

Q. In triangle

A B C

, If

tan (A / 2) = 5 / 6

and

tan (B / 2) = 20 / 37

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Q. IN TRIANGLE ABC , tanA/2=5/6 , tanB/2=20/37 , tanC/2 = ???

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tan \frac{A}{2} = \frac{5}{6}

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tan \frac{A}{2} = \frac{5}{6}, tan \frac{B}{2} = \frac{20}{37}

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In a △ABC, if tanA2=56 and tanB2=2037,then

The correct option is B a>b>c tanA2>tanB2 or A2>B2 or A>B tan(A+B2)=56+20371−56×2037=305122 Or tanC2=122305, As 2037>122305 we Get tanB2>tanC2 ⇒B>C ∴A>B>C ⇒a>b>c

In a $△ A B C$ , if $t a n \frac{A}{2} = \frac{5}{6} a n d t a n \frac{B}{2} = \frac{20}{37}$ ,then