Question

if sin(A-B)=1/2, cos(A+B)=1/2, 0<A+B=90, A>B find A and B​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given :-

• Sin (A - B) = ½
• Cos (A + B) = ½

To find :-

• The value of A and B = ?

Solution :-

Sin (A - B) = ½

We know that ½ is the value of Sin 30°

so,

➟ Sin (A - B) = Sin 30°

➟ A - B = 30° ...........................(i)

Then,

Cos (A + B) = ½

we know that ½ is the value of cos 60°

so,

➟ Cos (A + B) = Cos 60°

➟ A + B = 60° ..........................(ii)

Adding eq (i) and eq (ii),

(A - B) + (A + B) = 30° + 60°

➟ A - B + A + B = 90°

➟ A + A = 90°

➟ 2A = 90°

➟ A = $\bf\dfrac{90}{2}$

➟ A = 45°

Putting the value of A in eq (ii),

A + B = 60°

➟ 45° + B = 60°

➟ B = 60° - 45°

➟ B = 15°

Hence,the value of A and B will be 45° and 15°