Question

Q:-If tan θ =12/5 ,then show that 5 cos θ + 12 sin θ = 13
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Answer 1

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

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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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Answer 2

Step-by-step explanation:

Answer

Step-by-step explanation:

so 5 cosx = 13-12 sinx

squaring on both sides we get,

25 cos²x = 169 + 144 sin²x - 312 sinx

in case of cos²x we substitute (1-sin²x), as sin²x + cos²x = 1

equation will be 169 sin²x - 312 sinx + 144 = 0

after using quadratic formula we get sinx = 312/338

so sinx = 12/13.