Question

Q:-If tan θ =12/5 ,then show that 5 cos θ + 12 sin θ = 13 solve this class 10 trigonometric Question
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Answer 1

Step-by-step explanation:

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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

=144+125=169

⟹h = 169² = 13⟹h= 169

=13

⟹cos \theta =b/h = 5/13⟹cosθ= h/b

= 13/5

⟹sin \theta = p/h = 13/11

⟹sinθ= h/p

= 13/12

Now \: 5 \times \frac{5}{13} + 12 \times \frac{12}{13} = 13Now5×

13

5

+12×

13

12

=13

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

13

25

+

13

144

=13

=13

13 = 1313=13

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

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HOPE IT HELPS YOU..

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