Math, asked by sampachou101977, 11 months ago

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

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Answered by tennetiraj86
2

Answer:

answer for the given problem is given

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Answered by Anonymous
29

\pink{\bold{\underline{ ✪ UPSC-ASPIRANT✪ }}}

\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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HOPE IT HELPS YOU..

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Thankyou:)

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