Question

Q1. If sin (A - B) = ½
and cos(A+B)=½
0°< A+B < 90°, find A and B​

Answer 1

Here's your answer -

A = 45° and B = 15°

Step-by-step explanation:

sin (A-B) = 1/2

sin (A-B) = sin 30°

A-B= 30° .........(i)

cos(A+B) = 1/2

cos(A+B) = cos 60°

A+B = 60°. ..........(ii)

Solving (i) and (ii) -

A = 45°

B = 15°

Answer 2

Sin(A-B) = 1/2

but we know  that

sin 30 = 1/2

therefore, A-B = 30 .................... (1)

also , cos (A+B) = 1/2

but we know  that cos 60 = 1/2

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

Solving (1) & (2)

A + B = 60

A - B = 30

-     +      +

= 2B = 90

B = 90/2 = 45

Now, A+B = 60

= A + 45 = 60

= A = 60 - 45 = 15

Therefore A = 15 and B = 45.

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