First slide

Compound angles

Question

If $\sin (θ + α) = \cos (θ + α)$ then $\tan θ =$

Moderate

A

$\frac{1 + \tan α}{1 - \tan α}$
B

$\frac{1 + \sin α}{1 - \sin α}$
C

$\frac{1 - \tan α}{1 + \tan α}$
D

$\frac{1 + \cos α}{1 - \cos α}$

Solution

$\frac{\sin (θ + α)}{\cos (θ + α)} = 1 \Rightarrow$ $\tan (θ + α) = 1 \Rightarrow \tan α + \tan α = 1 - \tan θ \tan α$
$\Rightarrow \tan θ (1 + \tan α) = 1 - \tan α$
$\Rightarrow \tan θ = \frac{1 - \tan α}{1 + \tan α}$

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