Question

If $\sec \theta =13$, prove that $\sin \theta =\frac{12}{13}$

Answer 1

$sec\theta =\frac{5}{13}$

$sec\theta =\frac{1}{cos\theta }=\frac{13}{5}$

$cos\theta =\frac{5}{13}$

$sin\theta =\sqrt{1-{cos}^2\theta }$

$sin\theta =\sqrt{1-\frac{25}{169}}$

$sin\theta =\sqrt{\frac{169-25}{169}}$

$sin\theta =\sqrt{\frac{144}{169}}$

$sin\theta =\frac{12}{13}$