Question

if 3tanthheta=5 then find 3sintheta-5costhita/ 3sinthita+5costhita

Answer 1

$Given \:3tan \theta = 5$

$\implies 3\Big(\frac{sin \theta}{cos \theta}\Big) = 5$

$\implies 3sin \theta = 5 cos \theta \: ---(1)$

$Now, Value \:of \: \frac{3sin\theta - 5cos \theta}{3sin \theta + 5cos \theta } \\= \frac{5cos \theta - 5cos \theta}{5cos\theta + 5cos \theta } \: [ Form \:(1) ] \\= \frac{0}{10cos\theta} \\= 0$

Therefore.,

$\red {Value \:of \: \frac{3sin\theta - 5cos \theta}{3sin \theta + 5cos \theta }}\green {= 0 }$

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Answer 2

Answer:

$\frac{3sin\theta-5cos\thete}{3sin\theta+5cos\thete} =0$

Step-by-step explanation:

Given that

$3tan\theta=5\\\\=> 3*\frac{sin\theta}{cos\theta}=5\\\\ =>3sin\thete=5cos\theta$

Substitute this in required expression $\frac{3sin\theta-5cos\thete}{3sin\theta+5cos\thete}$

$=>\frac{5cos\theta-5cos\thete}{5cos\theta+5cos\thete}\\\\=>\frac{0}{10cos\thete} \\\\=>0$

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