Question

In triangle ABC, right-angled at B, if tan A =
$\frac{1}{ \sqrt{3} }$
find the value of :

(i) sin A cos C + cos A sin C
(ii) cos A cos C - sin A sin C
​

Answer 1

Answer:-

1)1

2)0

Solution:-

tan A=1/√3=BC/AB

BC=1

AB=√3

AC²=BC²+AB²

AC²=1²+√3²

AC=√1+3

AC=√4

AC=2

i)sin A cos C+cos A sin C=1/2×1/2+√3/2×√3/2=1/4+3/4=4/4=1

ii)cosA cos C -sin A sin C=√3/2×1/2-1/2×√3/2=√3-√3/4=0/4=0

@Indian Army