Question

if 5cot theta =3 find the value of 5sin thieta -3cos thita /4sin theta +3cos theta

Answer 1

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Answer 2

The value of$\dfrac{5\sin \theta -3\cos \theta}{4\sin \theta +3\cos \theta}=\dfrac{16}{29}$.

Step-by-step explanation:

We have,

$5\cot \theta=3$

∴  $\cot \theta=\dfrac{3}{5}$

To find, the value of $\dfrac{5\sin \theta -3\cos \theta}{4\sin \theta +3\cos \theta}$=?

∴ $\dfrac{5\sin \theta -3\cos \theta}{4\sin \theta +3\cos \theta}$

Dividing numerator and denominator by $\sin \theta,$ we get

$\dfrac{\dfrac{5\sin \theta -3\cos \theta}{\sin \theta}}{\dfrac{4\sin \theta +3\cos \theta}{\sin \theta}}$

$=\dfrac{5-3\cot \theta}{4+3\cot \theta}$

Put $\cot \theta=\dfrac{3}{5} ,$ we get

∴ $\dfrac{5-3\times \dfrac{3}{5}}{4+3\times \dfrac{3}{5}}$

$=\dfrac{5-\dfrac{9}{5}}{4+\dfrac{9}{5}}$

$=\dfrac{\dfrac{25-9}{5}}{\dfrac{20+9}{5}}$

$=\dfrac{16}{29}$

Hence, the value of$\dfrac{5\sin \theta -3\cos \theta}{4\sin \theta +3\cos \theta}=\dfrac{16}{29}$.