If 5tan θ = 4, then frac{{5sin θ - 3cos θ }}{{5sin θ + 2cos θ }} =

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3.Trigonometrical Ratios, Functions and Identities

easy

If $5\tan \theta = 4,$ then $\frac{{5\sin \theta - 3\cos \theta }}{{5\sin \theta + 2\cos \theta }} = $

$0$

$1$

$1/6$

$6$

Solution

$\therefore \sin \theta = \frac{4}{{\sqrt {41} }}$ and

$\cos \theta = \frac{5}{{\sqrt {41} }}$

$\frac{{5\sin \theta – 3\cos \theta }}{{5\sin \theta + 2\cos \theta }}$

$= \frac{{5 \times \frac{4}{{\sqrt {41} }} – 3 \times \frac{5}{{\sqrt {41} }}}}{{5 \times \frac{4}{{\sqrt {41} }} + 2 \times \frac{5}{{\sqrt {41} }}}}$

$\frac{{20 – 15}}{{20 + 10}} = \frac{5}{{30}} = \frac{1}{6}$.

Standard 11

Mathematics

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hard

If $5\tan \theta = 4,$ then $\frac{{5\sin \theta - 3\cos \theta }}{{5\sin \theta + 2\cos \theta }} = $

Solution

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