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Question Number 21140 by oyshi last updated on 14/Sep/17

i f \tan β = \frac{2 \sin α \sin γ}{\sin (α + γ)}

s o p r o o f \cot γ + \cot α = 2 \cot β

Commented by $@ty@m last updated on 15/Sep/17

S t e p 1 . T a k e r e c i p r o c a l o f b o t h s i d e s .

S t e p 2 . M u l t i p l y b o t h s i d e s b y 2

S t e p 3 . A p p l y f o r m u l a f o r \sin (α + γ)

S t e p 4 . U s e i d e n t i t y \frac{A + B}{C} = \frac{A}{C} + \frac{B}{C}

Answered by myintkhaing last updated on 15/Sep/17

\frac{1}{\tan β} = \frac{\sin (α + γ)}{2 \sin α \sin γ}

\cot β = \frac{\sin α \cos γ + \cos α \sin γ}{2 \sin α \sin γ}

2 \cot β = \cot γ + \cot α