If tan 7 θ · tan 3 θ=1, then value of θ is ..........

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8. Introduction to Trigonometry

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If $\tan 7 \theta \cdot \tan 3 \theta=1,$ then the value of $\theta$ is ..........

A

$30$

B

$18$

C

$15$

D

$9$

Solution

$\tan 7 \theta \cdot \tan 3 \theta=1$

$\therefore \tan 7 \theta=\frac{1}{\tan 3 \theta}$

$\therefore \tan 7 \theta=\cot 3 \theta$

$\therefore \tan 7 \theta=\tan (90-3 \theta)$

$\therefore 7 \theta=90-3 \theta$

$\therefore 10 \theta=90 \quad \therefore \theta=9$

Standard 10

Mathematics

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