Question

tan theeta = 7/12 then find (sin theeta+cos theeta)/(3sintheeta+4costheeta)​

Answer 1

Answer:

19/69

Step-by-step explanation:

it's simple divide costheta to each term and put the value of tan theta

Answer 2

Answer:

${\bold{\therefore \frac{ sin\theta + cos \theta }{ 3 sin\theta + 4 cos\theta } = \frac{19}{33} }}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given

about trigonometry.

• We have to find the given value by using some trigo functions.

$\underline \bold{Given : } \\ \implies \tan\theta = \frac{7}{12} \\ \\ \underline \bold{To \: Find : } \\ \implies \frac{ \sin \theta + \cos \theta }{3 \sin \theta + 4\cos \theta } = ?$

• According to given questions :

$\bold{using \: trigonometric \: functions} \\ \implies \tan \theta = \frac{7}{12} \\ \implies \cot \theta = \frac{1}{ \tan\theta } \\ \implies \cot\theta = \frac{1}{ \frac{7}{12} } \\ \implies\cot \theta = \frac{12}{7} \\ \\ \implies \frac{ \sin\theta + \cos \theta }{3 \sin \theta + 4\cos \theta } \\ \bold{dividing \: } \bold{sin\theta} \bold{ \: in \: numerator \: and \: denominator }\\ \implies \frac{ \frac{ \sin \theta }{ \sin\theta} + \frac{ \cos \theta }{ \sin \theta } }{ \frac{3 \sin \theta }{ \sin \theta } + \frac{ 4\cos \theta }{ \sin \theta } } \\ \implies \frac{1 + \cot\theta}{3 + 4\cot\theta} \\ \implies \frac{1 + \frac{12}{7} }{3 + 4\times\frac{12}{7} } \\ \implies \frac{ \frac{7 + 12}{7} }{ \frac{21 + 48}{7} } \\ \implies \frac{19}{7} \times \frac{7}{69} \\ \bold{\implies \frac{19}{69}} \\ \\ \bold{\therefore \frac{ sin\theta + cos \theta }{ 3 sin\theta + cos\theta } = \frac{19}{69} }$