Question

if tan theta=5/13 and π< theta<3π/2 find value of sec theta and cosec theta​

Answer 1

given★

• $\pink\implies\tan( \theta) = \frac{5}{13}$
• where

• $\pi < \theta \: < \frac{3\pi}{2}$

find value★

• $\implies \red \sec \theta \:$

• $\implies \red\cosec \theta$

solution★

• we know that

• $\tan( \theta) = \frac{p}{b} = \frac{5}{13}$

• $\red p = 5$
• $and \: \: \red b = 13$

• as we know that

• $\implies \star\red{ h {}^{ {}^{2} } = p {}^{2} + b {}^{2} }$

• $\implies \star \pink{h = \sqrt{p {}^{2} + b {}^{2} } }$

• put value p and b

• $\implies \: h = \sqrt{5 {}^{2} + 13 {}^{2} }$

• $\implies \: h = \sqrt{25 + 169}$

• $\implies h = \sqrt{194}$

• we know that

• $\implies \: \sec( \theta) = \frac{h}{b} = \frac{ \sqrt{194} }{13}$

• $\implies \: \cosec( \theta) = \frac{h}{p} = \frac{ \sqrt{194} }{5}$

answer

• $\red \sec \theta = \frac{ \sqrt{194} }{13}$

• $\red \cosec\theta = \frac{ \sqrt{194} }{5}$

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I hope it helps you

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