Question

given a right angled triangle ABC right angled at C in which cot a = 2 root 3 and cot B equals to 1 / root 3 show that Cos A into cos B minus sin a into Sin B=zero

Answer 1

Draw a unit circle with center O. Let a central angle with initial side OP and terminal side OQ contain x radians (that is, the arc PQ has length x). Drop a perpendicular from Q to OP meeting it at R. Then OR = cos(x) and RQ = sin(x). If those directed line segments are up or to the right, the lengths are positive. If they are down or to the left, the lengths are negative.