CBSE Class 10 Answered

Q 9)     triangle ABC rt angled at B   given tan A = 1 / 3

   tan A =BC / AB = 1 /  3    In triangle ABC  AC = 2 by Pythagores them.

   sin A =1/2 , cos A =  3 / 2 , sin C =  3 / 2 , cos C = 1/2

   sinA cos C + cos A sin C = 1/2 x 1/ 2 +  3 / 2 x  3 / 2

                                                = 1 /4 + 3 / 4 = 1

 cos A cos C - sin A sin C =  3 / 2 x 1/2 - 1 /2 x  3 / 2

                                              =  3 / 4 -  3/ 4 = 0

Q 10 )   I n triangle PQR rt angled at Q PQ = 5 and PR + QR = 25  therefore PR = 25 - QR

  using Pythagores them.     PR ²= QR ² + PQ²

                                  ( 25 - QR )² = QR ² + (5)²

                              625 + QR² - 50 QR = QR² + 25

                                  QR = 12 and PR = 13

       sin P =12 / 13 ,cos P = 5 / 13 , tan P =12 / 5