Question

If 5 cos θ + 12 sin θ = 13, then show that, tan θ =12/5 .

Answer 1

Answer:

answer for the given problem is given

Answer 2

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$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-If 5 cos θ + 12 sin θ = 13, then show that, tan θ =12/5 .

$\huge\tt\underline\blue{Answer }$

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$⟹tan \theta = \frac{p}{b} = \frac{12}{5}$

$⟹ {h}^{2} = {p}^{2} + {b}^{2}$

$⟹ {h}^{2} = 144 + 125 = 169$

$⟹h = \sqrt{169} = 13$

$⟹cos \theta = \frac{b}{h} = \frac{5}{13}$

$⟹sin \theta = \frac{p}{h} = \frac{12}{13}$

$Now \: 5 \times \frac{5}{13} + 12 \times \frac{12}{13} = 13$

$⟹ \frac{25}{13} + \frac{144}{13} = 13$

$⟹ \frac{169}{13} = 13$

$13 = 13$

From above it is proved that $tan\theta=12/5$

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