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

Prove that:

$2 \sin ^{2} \frac{\pi}{6}+\cos ec ^{2} \frac{7 \pi}{6} \cos ^{2} \frac{\pi}{3}=\frac{3}{2}$

medium

Find the values of other five trigonometric functions if $\sec x=\frac{13}{5}, x$ lies in fourth quadrant.

hard

If the arcs of the same length in two circles $S_1$ and $S_2$ subtend angles $75^o $ and $120^o $ respectively at the centre. The ratio $\frac{{{S_1}}}{{{S_2}}}$ is equal to

normal

Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.

$10 \,cm$

easy

$\frac{{1 + \sin A – \cos A}}{{1 + \sin A + \cos A}} =$

medium

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

Solution

Similar Questions

Prove that: $2 \sin ^{2} \frac{\pi}{6}+\cos ec ^{2} \frac{7 \pi}{6} \cos ^{2} \frac{\pi}{3}=\frac{3}{2}$

Find the values of other five trigonometric functions if $\sec x=\frac{13}{5}, x$ lies in fourth quadrant.

If the arcs of the same length in two circles $S_1$ and $S_2$ subtend angles $75^o $ and $120^o $ respectively at the centre. The ratio $\frac{{{S_1}}}{{{S_2}}}$ is equal to

Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length. $10 \,cm$

$\frac{{1 + \sin A – \cos A}}{{1 + \sin A + \cos A}} =$

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Prove that:

$2 \sin ^{2} \frac{\pi}{6}+\cos ec ^{2} \frac{7 \pi}{6} \cos ^{2} \frac{\pi}{3}=\frac{3}{2}$

Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.

$10 \,cm$