First slide

Multiple and sub- multiple Angles

Question

$x = \cot 6 ° \cot 42 °, y = \tan 66 ° \tan 78 °$ then $\frac{y}{x} =$

Moderate

A

2
B

1
C

4
D

5

Solution

$\begin{array}{l} x = \cot 6 ° \cot 42 °, y = \tan 66 ° \tan 78 ° \\ \frac{y}{x} = \tan 6 ° \tan 42 ° \tan 66 ° \tan 78 ° \\ = \frac{(\tan 6 ° \tan 54 ° \tan 66 °) (\tan 18 ° \tan 42 ° \tan 78 °)}{\tan 54 ° \tan 18 °} \\ = \frac{\tan 18 ° \tan 54 °}{\tan 54 ° \tan 18 °} (∵ \tan θ \tan (60^{\circ} - θ) an (60^{\circ} + θ) = \tan 3 θ) \\ = 1 \end{array}$

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