Question

Sin (A+B)=1 and Sin(A-B)=1/2. find A and B

Answer 1

Answer:

A=60

B=30

Step-by-step explanation:

sin(a+b)=1

sin(1)=90

(a+b)=90

sin(a-b)=1/2

sin(1/2)=30

(a-b)=30

a+b=90

a-b=30

2a=120

a=60

substitute in eqvation a-b=30

a-b=30

60-b=30

b=60-30

b=30

Answer 2

A = 60     B = 30

Given:

• Sin (A + B) = 1
• Sin (A - B) = 1/2

To find: A and B

Step by step explanation:

→ Basic concepts used:

• Inverse trigonometric properties.
• Elimination method

⇒ Sin (A + B) = 1
⇒ (A + B) = $sin^{-1}$ (1)
⇒ A + B = 90                                                          (1)

⇒ Sin (A - B) = 1/2
⇒ (A - B) = $sin^{-1}$ (1)
⇒ A - B = 30                                                          (2)

Now, adding (1) and (2)
A + B = 90
A - B = 30
we get, 2A = 120     ⇒ A = 120/2
             A = 60

Now, substituting the value of A in (1) we get,
60 + B = 90             ⇒ B = 90 - 60
            B = 30

∴ The final values of A and B are 60 and 30 respectively.

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