Question

If tan a equal to 3 by 4 find 1 by sin a + 1 by cos c

Answer 1

Answer:

answr

search

What would you like to ask?

MATHS

In triangle ABC, right-angled at B, if tanA=

3

1

, find the value of

(i) sinAcosC+cosAsinC

(ii) cosAcosC−sinAsinC

Share

Study later

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