If 5 θ is measure of acute angle and cos θ=sin 5 θ, then value of θ is ldots ldots ldots ldots

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8. Introduction to Trigonometry

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If $5 \theta$ is the measure of acute angle and $\cos \theta=\sin 5 \theta,$ then the value of $\theta$ is $\ldots \ldots \ldots \ldots$

A

$5$

B

$10$

C

$15$

D

$50$

Solution

$\cos \theta=\sin 5 \theta$

$\therefore \cos \theta=\cos (90-5 \theta)$

$\therefore \theta=90-5 \theta$

$\therefore \theta+5 \theta=90$

$\therefore 6 \theta=90$

$\therefore \theta=15$

Standard 10

Mathematics

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