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Question: In a ∆ABC, if \(\tan\frac{A}{2}\) = \(\frac{5}{6}\) and \(\tan\frac{B}{2}\) = \(\frac{20}{37}\), the...

In a ∆ABC, if tan⁡A2\tan\frac{A}{2} = 56\frac{5}{6} and tan⁡B2\tan\frac{B}{2} = 2037\frac{20}{37}, then –

A

a> b > c

B

a < b < c

C

b < c < a

D

c > a > b

Answer

a> b > c

Explanation

Solution

Clearly, >

∴ ⇒ A > B

Now, = 56+20371−56⋅2037\frac { \frac { 5 } { 6 } + \frac { 20 } { 37 } } { 1 - \frac { 5 } { 6 } \cdot \frac { 20 } { 37 } } = 305122\frac { 305 } { 122 }

⇒ = 122305\frac { 122 } { 305 }

Also, 2037>122305\frac { 20 } { 37 } > \frac { 122 } { 305 }

⇒

⇒ B2>C2\frac { B } { 2 } > \frac { C } { 2 } ⇒ B > C

∴ A > B > C

∴ a > b > c.