Question

9. If a cos 0 + b sin 0 = 12 and a sin 0 - 5 cos = 5, then a2 + b2 is equal to: .. (a) 13 (6) 12 (c) 144 (d) 169​

Answer 1

Answer:

ans. (d) 169

a cos 0 + b sin 0 = 12 ----(1)

a sin 0 - b cos 0 = 5 ----(2)

equate both the equation (1) and (2)

(a cos 0 + b sin 0 )² + (a sin 0 - b cos 0 )²=12²+4²

a² cos²0 + 2 ab sin 0 cos 0 + b² sin² 0 + a² sin² 0 -2ab sin0 cos 0 + b² cos² 0 = 144 + 25

a² ( sin² 0 + cos² 0 ) + b² (sin² 0 + cos² ) = 169

a² + b² = 169