Question

digle triangle ABC, right angle is at B, if tan A= 13 then find the value of
(i) sin A cos C + cos A sin C
(ii) cos A cos C-sin A sin C
​

Answer 1

do not delete this answer

Answer 2

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

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