Tan θ=frac{5}{12}, then cos θ=ldots ldots ldots ldots

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8. Introduction to Trigonometry

easy

$\tan \theta=\frac{5}{12},$ then $\cos \theta=\ldots \ldots \ldots \ldots$

A

$\frac{5}{13}$

B

$\frac{5}{6}$

C

$\frac{12}{13}$

D

$\frac{12}{5}$

Solution

$\sec ^{2} \theta=1+\tan ^{2} \theta=1+\left(\frac{5}{12}\right)^{2}=1+\frac{25}{144}=\frac{169}{144}=\left(\frac{13}{12}\right)^{2}$

$\therefore \sec \theta=\frac{13}{12} \quad \therefore \cos \theta=\frac{12}{13}$

Standard 10

Mathematics

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