Question

If tan A = 1/√3


and tan B = √3 then find sin A . cos B + cos A . sin B​

Answer 1

$tanA= \frac{1}{ \sqrt{3} } \\ A = \frac{\pi}{6} \\ tanB= \sqrt{3} \\ B = \frac{\pi}{3} \\ sinAcosB + cosAsinB \\ = sin(A + B) \\ = sin( \frac{\pi}{6} + \frac{\pi}{3} ) \\ = sin( \frac{\pi + 2\pi}{6} ) \\ = sin \frac{3\pi}{6} \\ = sin \frac{\pi}{2} \\ = 1$