Question

If tan A = 1/√3


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

Answer 1

$tana = \frac{1}{ \sqrt{3} } \\ a = \frac{\pi}{6} \\ tanb = \sqrt{3} \\ b = \frac{\pi}{3} \\ sinacosb + cosasinb \\ = sin(a + b) \\ = sin( \frac{\pi}{6} + \frac{\pi}{3} ) \\ = sin( \frac{\pi + 2\pi}{6} ) \\ = sin \frac{3\pi}{6} \\ = sin \frac{\pi}{2} \\ = 1$