Question

If sin (A – B) = 1/2, cos (A + B) = 1/2, find A and B.​

Answer 1

EXPLANATION.

⇒ sin(A - B) = 1/2. - - - - - (1).

⇒ cos(A + B) = 1/2. - - - - - (2).

As we know that,

We can write equation as,

⇒ sin(A - B) = sin(30°).

⇒ cos(A + B) = cos(60°).

Now, we write equation as,

⇒ A - B = 30°.

⇒ A + B = 60°.

Adding both the equation, we get.

⇒ 2A = 90°.

⇒ A = 45°.

Put the value of A = 45° in equation, we get.

⇒ A + B = 60°.

⇒ 45° + B = 60°.

⇒ B = 60° - 45°.

⇒ B = 15°.

Values of A = 45°   and   B = 15°.

Answer 2

given data :

sin(A - B) = 1/2

cos(A + B) = 1/2

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to find :

values of A,B

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Solution :

sin(A - B) = ½

⇒ sin(A - B) = sin 30° [°.° sin 30 = ½]

⇒ A - B = 30°

⇒ A = 30 + B ___eq(1)

cos(A + B) = ½

⇒ cos(A + B) = cos 60° [°.° cos 60 = ½]

⇒ A + B = 60

• from eq(1),

⇒ 30 + B + B = 60

⇒ 2B = 30

⇒ B = 15°

then,

⇒ A = 30 + 15

⇒ A = 45°