Question

9. In triangle ABC, right-angled at B, if tan A= = find the value of: :
3
(i) sin A cos C + cos A sin C
(ii) cos A cos C - sin A sin C​

Answer 1

Step-by-step explanation:

In △ABC,

∠B=90o, tanA=31=ABBC

Let BC =1x,AB=3x

AC2=AB2+BC2

AC2=(3x)2+(x)2=4x2

AC=2x

(i) sinAcosC+cosAsinC=21×21+23×23=41+43=1

(ii) cosAcosC−sinAsinC=23