Correct Answer - Option 2 : 7
Concept:
\(\rm tan (A + B) = \frac{tan A + tan B }{1 - tan A\times tan B }\)
\(\rm \frac{sin \theta }{cos \theta } = tan \theta \)
Calculation:
3 cos θ = 4 sin θ
\(\rm \frac{3}{4} = \frac{sin \theta }{cos \theta } \)
\(\rm \frac{3}{4} = tan \theta \)
\(\rm tan (45^{\circ} + \theta) = \frac{tan 45^{\circ} + tan \theta }{1 - tan 45^{\circ}\times tan \theta }\)
= \(\rm \frac{1 + \frac{3}{4} }{1 - 1 \times \frac{3}{4}} \)
= \(\rm \frac{1 + \frac{3}{4} }{1 - \frac{3}{4}}\)
= \(\rm \frac{\frac{7}{4}}{\frac{1}{4}}\)
= 7
