Question

9. In triangle ABC, right-angled at B, if an A= 1/√3,
find the value of:

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

Answer 1

In △ABC,

∠B=90o

, tanA= 31

= ABBC

Let BC =1x,AB= 3x

AC

2

=AB

2

+BC

2

AC

2

=(

3

x)

2

+(x)

2

=4x

2

AC=2x

(i) sinAcosC+cosAsinC=

2

1

×

2

1

+

2

3

×

2

3

=

4

1

+

4

3

=1

(ii) cosAcosC−sinAsinC=

2

3

×

2

1

−

2

1

×

2

3

=

4

3

−

4

3

=0

solution