Question

5tan=3,find 5sin-3cos/5sin+3cos

Answer 1

hey ,here is the solution

Answer 2

$\huge \sf \underline{Answer}:$

$\large ::\implies\sf \frac{5Sin\theta-3Cos\theta}{5Sin\theta+3Cos\theta} = 0$

$\\ \\ \huge \sf \underline{Solution}:$

$\large \sf \underline{Given}:$

$\large \bf 5tan\theta=3$

$\\ \large \sf \underline{To \: find}:$

$\sf\bigstar\large \frac{5Sin\theta-3Cos\theta}{5Sin\theta+3Cos\theta}$

So,

$\large \sf 5tan\theta=3 \\ \sf \implies tan\theta=\frac{3}{5} \\ \implies \frac{sin\theta}{Cos\theta}=\boxed{\sf \frac{3}{5}}$

Now ,

$\\ \large \implies\sf \frac{5Sin\theta-3Cos\theta}{5Sin\theta+3Cos\theta}$

$\sf \colorbox{skyblue}{Dividing \: Numerator \: and \: denominator \: by \: Cos\theta}$

$\\ \large\sf ::\implies \frac{5\frac{Sin\theta}{cos\theta}-3\frac{\cancel{Cos\theta}}{\cancel{cos\theta}}}{5\frac{Sin\theta}{cos\theta}+3\frac{\cancel{Cos\theta}}{\cancel{cos\theta}}}$

$\\ \bf Putting \frac{sin\theta}{cos\theta}=\frac{3}{5}$

$\\ \large :: \implies \frac{\cancel{5}×\frac{3}{\cancel{5}}-3}{\cancel{5}×\frac{3}{\cancel{5}}+3} \\ \\ \large\implies\sf\frac{3-3}{3+3}\\ \\ \large\implies\sf\frac{0}{6} \\ \\ \large\implies\sf 0$

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