Question

If sin(A+B)=12√ and cos(A−B)=12√sin(A+B)=12 and cos(A−B)=12 , then ∠B= ​

Answer 1

Step-by-step explanation:

Given, sin(A−B)=

2

1

cos(A+B)=

2

1

0

∘

<A+B≤90

∘

and A<B,

We know that, sin30

∘

=

2

1

and cos60

∘

=

2

1

Consider,

sin(A−B)=

2

1

and sin30

∘

=

2

1

⟹(A−B)=30

∘

---------------(i)

Consider,

cos(A+B)=

2

1

and cos60

∘

=

2

1

⟹(A+B)=60

∘

---------------(ii)

Solve (i) and (ii) :

(A−B)=30

∘

(A+B)=60

∘

Adding both equations,

2A=90

∘

A=

2

90

∘

=45

∘

From (ii)

(A+B)=60

∘

Also, A=45

∘

B=60

∘

−45

∘

B=15

∘

∴A=45

∘

,B=15

∘