If in ∆ABC, ∠C = 90° and tan A = 3/4 , prove that sin A cos B + cos A sin B = 1.

Let ABC be a right angled triangle with ∠C = 90°. Given, tan A = By formula, ⇒ Let BC = 3x and AC = 4x. In △ABC, ⇒ AB 2 = AC 2 + BC 2 ⇒ AB 2 = (4x) 2 + (3x) 2 ⇒ AB 2 = 16x 2 + 9x 2 ⇒ AB 2 = 25x 2 ⇒ AB = ⇒ AB = 5x. By formula, Substituting values in L.H.S. of sin A cos B + cos A sin B = 1. Since, L.H.S. = R.H.S. Hence, proved that sin A cos B + cos A sin B = 1.