8. Introduction to Trigonometry
medium

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

A

$\frac{22}{13}$

B

$2$

C

$\frac{26}{9}$

D

$\frac{7}{2}$

Solution

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

($\because $ Dividing each term of numerator and denominator by $\cos \theta, \cos \theta \neq 0$ )

$=\frac{5 \tan \theta+2}{3 \tan \theta-1}=\frac{5\left(\frac{4}{3}\right)+2}{3\left(\frac{4}{3}\right)-1}=\frac{\frac{20}{3}+2}{4-1}=\frac{20+6}{3 \times 3}=\frac{26}{9}$

Standard 10
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.