First slide

Compound angles

Question

If $0 < θ < \frac{π}{2}, \tan θ = \frac{\cos 29^{0} + \sin 29^{0}}{\cos 29^{0} - \sin 29^{0}}$ then $θ =$

Moderate

A

$16^{0}$
B

$74^{0}$
C

$37^{0}$
D

$8^{0}$

Solution

$\tan θ = \frac{\cos 29 + \sin 29}{\cos 29 - \sin 29} d e v i d e n u m e r a t o r a n d d e n o m i n a t o r w i t h \cos 29$
$\tan θ = \frac{1 + \tan 29}{1 - \tan 29} = \tan (45 + 29)$

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