(A) Given,$\theta$ lies in the first quadrant and $5 \tan \theta = 4$. Dividing the numerator and denominator of the expression by $\cos \theta$,we ge

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(A) Given,$\theta$ lies in the first quadrant and $5 \tan \theta = 4$. Dividing the numerator and denominator of the expression by $\cos \theta$,we get: $\frac{5 \tan \theta - 3}{\tan \theta + 2}$ Substituting $\tan \theta = \frac{4}{5}$: $\frac{5(\frac{4}{5}) - 3}{\frac{4}{5} + 2} = \frac{4 - 3}{\frac{4 + 10}{5}} = \frac{1}{\frac{14}{5}} = \frac{5}{14}$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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If $\theta$ lies in the first quadrant and $5 \tan \theta = 4$,then $\frac{5 \sin \theta - 3 \cos \theta}{\sin \theta + 2 \cos \theta}$ is equal to

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A
$\frac{5}{14}$
B
$\frac{3}{14}$
C
$\frac{1}{14}$
D
$0$

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Trigonometrical Ratios, Functions and Identities

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Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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If $\theta$ lies in the first quadrant and $5 \tan \theta = 4$,then $\frac{5 \sin \theta - 3 \cos \theta}{\sin \theta + 2 \cos \theta}$ is equal to

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If $\frac{\cos A}{3} = \frac{\cos B}{4} = \frac{1}{5}$,$-\frac{\pi}{2} < A < 0$,and $-\frac{\pi}{2} < B < 0$,then the value of $2 \sin A + 4 \sin B$ is

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