First slide

Multiple and sub- multiple Angles

Question

If $\frac{3 \sin 2 θ}{5 + 4 \cos 2 θ} = 1$ then the value of $\tan θ$ is equal to

Moderate

A

1
B

$\frac{1}{3}$
C

3
D

none of these

Solution

$\begin{array}{l} \frac{6 \sin θ \cos θ}{8 \cos^{2} θ + 1} = \frac{6 \tan θ}{9 + \tan^{2} θ} = 1 \\ \Rightarrow \tan^{2} θ - 6 \tan θ + 9 = 0 \\ \Rightarrow \tan θ = 3 \end{array}$

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