Question

10. Find measure of the angles A and B. if cos(A-B)
=
and sin(A + B)
2​

Answer 1

Answer:

We know that

sin60^{\circ}=\frac{\sqrt{3}}{2}sin60

∘

=

2

3

cos30^{\circ}=\frac{\sqrt{3}}{2}cos30

∘

=

2

3

Using the values

cos(A-B)=cos30^{\circ}cos(A−B)=cos30

∘

A-B=30A−B=30 ...(1)

sin(A+B)=sin60^{\circ}sin(A+B)=sin60

∘

A+B=60A+B=60 ...(2)

Adding equation (1) and (2) we get

2A=902A=90

A=45^{\circ}A=45

∘

Substitute the value of A in equation (1)

45-B=3045−B=30

B=45-30=15^{\circ}B=45−30=15

∘

Hence, the measure of angles

A=45^{\circ}A=45

∘

and B=15^{\circ}B=15

∘