If 3 θ is measure of acute angle and sin 3 θ=cos (θ-26), then value of θ is ldots ldots ldots ld

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8. Introduction to Trigonometry

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If $3 \theta$ is the measure of acute angle and $\sin 3 \theta=\cos (\theta-26),$ then the value of $\theta$ is $\ldots \ldots \ldots \ldots$

A

$64$

B

$16$

C

$29$

D

$58$

Solution

$\sin 3 \theta=\cos (\theta-26)$

$\therefore \cos (90-3 \theta)=\cos (\theta-26)$

$\therefore 90-3 \theta=\theta-26$

$\therefore 90+26=4 \theta$

$\therefore 4 \theta=116$

$\therefore \theta=29$

Standard 10

Mathematics

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