Question

If A and B are acute angles such that cos (A+B) = 1/2 = sin (A-B), find the values of A and B.​

Answer 1

Correct QuestioN :

If A and B are acute angles such that Cos(A+B) = 1/2 and Sin (A-B) = 1/2, find the values of A and B.

SolutioN :

Sin( A - B ) = 1/2.

Sin( A - B ) = Sin 30°

→ A - B = 30°. ____1

$\rule{90}2$

Cos( A + B ) = 1/2.

→ Cos( A + B ) = Cos 60°.

→ A + B = 60.____2

$\rule{90}2$

★ Now, By Elimination Method.

A + B = 60.

A - B = 30.

________

2A = 90.

________

→ A = 45.

$\rule{90}2$

Let's Find the value of B.

Putting value of A in Equation 1.

→ A - B = 30.

→ 45 - B = 30.

→ - B = - 15.

→ B = 15.

Therefore, the value of A is 45 and B is 15.

Answer 2

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