+ sin = , and (ii) cos – sin = ( )( ) . Fig. . Example : In a right triangle ABC, right-angled at B, if tan A = , then verify that sin A cos A = .
Solution : In ABC, tan A = BC AB = (see Fig . ) BC = AB Let AB = BC = k , where k is a positive number. Now, AC = ( ) ( ) Therefore, sin A = and cos A = So, sin A cos A = , which is the required value. Example : In OPQ, right-angled at P, OP = cm and OQ – PQ = cm (see Fig.
. ). Determine the values of sin Q and cos Q. Solution : In OPQ, we have OQ = OP + PQ ( + PQ) = OP + PQ + PQ + 2PQ = OP + PQ + 2PQ = PQ = cm and OQ = + PQ = cm So, sin Q = and cos Q = Fig.
. In ABC, right-angled at B, AB = cm, BC = cm. Determine : (i) sin A, cos A (ii) sin C, cos C . In Fig.
. , find tan P – cot R. . If sin A = , calculate cos A and tan A.
. Given cot A = , find sin A and sec A. . Given sec = , calculate all other trigonometric ratios.
. If A and B are acute angles such that cos A = cos B, then show that A = B. . If cot = , evaluate : (i) ( sin )( sin )