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Sin(A+B) = 1 and cos(A-B) = 1/2, then values of A&B ​

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456 cents Ilmari
Answer:

Given:-

  • Sin (A+B) = 1
  • Cos (A-B) = 1/2

Find:-

  • Value of A and B

Solution:-

Sin ( A + B) = 1

We know that, Sin 90° = 1

⇒ Sin (A+B) = Sin 90°

⇒ A+B = 90....(1)

Cos ( A-B ) = 1/2

We know that, Cos 60° = 1/2

⇒ Cos (A-B) = Cos 60°

⇒ A-B = 60....(2)

Add equation (1) and (2) :-

⇒ A + B + A - B = 90 + 60

⇒ 2A = 150

⇒ A = 150/2

⇒ A = 75

Now substitute the value of A in equation (1)

⇒ A + B = 90

⇒ 75 + B = 90

⇒ B = 90 - 75

⇒ B = 15

Therefore,

  • A = 75
  • B = 15
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