Question

sin (A+B) = 1, & sin (A-B) = 1/2 ; <A=? <B=? ​

Answer 1

EXPLANATION.

⇒ sin(A + B) = 1. - - - - - (1).

⇒ sin(A - B) = 1/2. - - - - - (2).

As we know that,

We can write equation as,

⇒ sin(A + B) = sin(90°). - - - - - (1).

⇒ sin(A - B) = sin(30°). - - - - - (2).

⇒ A + B = 90°. - - - - - (1).

⇒ A - B = 30°. - - - - - (2).

Adding equation (1) and (2), we get.

⇒ 2A = 120°.

⇒ A = 60°.

Put the value of A = 60° in the equation (1), we get.

⇒ 60° + B = 90°.

⇒ B = 90° - 60°.

⇒ B = 30°.

Values of A = 60°  and  B = 30°.

Answer 2

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☞ Question

sin(A+B) = 1, & sin (A-B) = 1/2 ; <A=? <B=?

➽ To find the value

➽ A = ?

➽ B = ?

➽ Answer

➽ sin ( A + B ) = sin (90°) --------(1)

➽ sin (A - B ) = sin (30°) ----------(2)

➽ A+B = 90° ---------(1)

➽ A-B = 30° ----------(2)

➺ Adding equation (1) and (2)

➽ 2A= 120°

➽ A =>60°

Value of A = 60°

➨ 60°+B = 90°

➨ B=90°-30°

➨ B = 30°

$\bold{ \gray{ \sf \to \: value \: \: of \: \: a \: = 60 \degree \: }} \\ \\ \bold{ \gray{ \sf \to \: value \: \: of \: \: a \: = 30 \degree} }$

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