First slide

Compound angles

Question

If $\tan β = 2 \sin αsin γcosec (α + γ)$ then $\cot α, \cot β, \cot γ$ are in

Moderate

A

A.P
B

G.P.
C

H.P
D

none of these

Solution

$\tan β = 2 \sin αsin γcosec (α + γ) = \frac{2 \sin αsin γ}{\sin (α + γ)}$
$\begin{array}{l} or \cot β = \frac{\sin (α + γ)}{2 \sin αsin γ} \\ or 2 \cot β = \frac{\sin αcos γ + \cos αsin γ}{\sin αsin γ} = \cot α + \cot γ \end{array}$
$or \cot α, \cot β, \cot γ are in A.P.$

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