Question

In triangle ABC right angled at B if sin A=12, find the value of sin C cos a- cos C sin A


PLEASE HELP

Answer 1

Answer:

Given that,

In △ABC,∠B=90

∘

and tanA=

3

1

=tan30

∘

⟹∠A=30

∘

Hence, ∠C=60

∘

(i)sinAcosC+cosAsinC=sin30

∘

cos60

∘

+cos30

∘

sin60

∘

=

2

1

×

2

1

+

2

3

×

2

3

=

4

1

+

4

3

=

4

4

=1

(ii)cosAcosC−sinAsinC=cos30

∘

cos60

∘

−sin30

∘

sin60

∘

=

2

3

×

2

1

−

2

1

×

2

3

=

4

3

−

4

3

=0