Question

if cos theta =5/13.find 5 tan theta+cos theta by 5 tan theta -12 cot theta​

Answer 1

$\huge\bigstar \: \huge\mathrm { \underline{ \purple{answer} }} \: \bigstar \: </p><p></p><p> \:$

Firstly , we will find the other side of the triangle,

that is, AB.

In △ABC,

• ∠B = 90°
• AC = 13
• CB = 5

➠ By Pythagorus Theorm,

➥ AC² = AB² + BC²

➥ 13² = AB² + 5²

➥ 169 = AB² + 25

➥ AB² = 169 - 25

➥ AB² = 144

∴ AB = 12

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Now ,

• tanΘ = 12/5

• cosΘ = 5/13

• cotΘ = 5/12

➠ Putting these values we get,

$\tt{ \frac{5tan \theta + cos \theta}{5tan \theta - 12cot \theta} } \\ \\ \implies \tt{ \frac{ \cancel5( \frac{12}{ \cancel5}) + \frac{5}{13} }{ \cancel5( \frac{12}{ \cancel5} ) - \cancel{12}( \frac{5}{ \cancel{12}}) } } \\ \\ \implies \tt{ \frac{12 + \frac{5}{13} }{12 -5 } } \\ \\ \implies \tt{ \frac{ \frac{12(13) + 5}{13} }{7} } \\ \\ \implies \tt{ \frac{ \frac{156 + 5}{13} }{7} } \\ \\ \implies \red{\tt{ \frac{161}{91} }}$

∴ The required answer is 161/91.