Question

If sin (A - B) =1/2 ,
cos (A+B) = 1/2 ,
0º < A+B ≤ 90°,
A > B, find A and B​

Answer 1

Answer:

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Step-by-step explanation:

cos(A+B) = 1/2

⇒cos (A+B) = cos(60)  (as 0<A+B<90)

⇒A+B = 60

sin(A-B) = 1/2

⇒sin(A-B) = sin(30) or sin (150)

⇒A-B = 30 or 150

Case:1

A - B = 30

A + B = 60

Solving we get, A = 45 and B = 15

A>B is satisfied.

Case:2

A - B = 150

A + B = 60

Solving, we get A = 105, B = -45

A>B is satisfied.

So the value of A can be 45 or 105

Answer 2

Answer:

A=45

B=15

Step-by-step explanation:

sin(A-B)=1/2

cos(A+B)=1/2

sin30=1/2

cos60=1/2

So

A+B=60

A-B=30

By these we can say that

A=45

B=15

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