First slide

Compound angles

Question

If $α, β, γ \in (0, \frac{π}{2})$ then the value of $\frac{\sin (α + β + γ)}{\sin α + \sin β + \sin γ}$ is

Moderate

A

$> 1$
B

$< 1$
C

$= 1$
D

$= 0$

Solution

$\begin{array}{l} W e h a v e \sin (α + β) < \sin α + \sin β for α,β∈ (0, \frac{π}{2}) \\ \Rightarrow \sin (α + β + γ) < \sin α + \sin β + \sin γ \\ \Rightarrow \frac{\sin (α + β + γ)}{\sin α + \sin β + \sin γ} < 1 \end{array}$

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