Question

if sin(A+B)=1/2 and cos(A-B)=1/2 then ∠A=?

Answer 1

Answer:

45 degrees or π/4

Step-by-step explanation:

Here sin(A+B) = 1/2

that means A+B = 30degrees......eq1

cos(A-B) = 1/2

that means A-B = 60degrees.......eq2

Solving eq1 and eq2

A = 45 degrees or π/4.

Answer 2

Given: sin (A + B) = 1/2 and cos (A - B) = 1/2.

To find: The value of A.

Answer:

Sine gives the value of 1/2 at an angle of 30°.

⇒ A + B = 30°.

Cosine gives the value of 1/2 at angle of 60°.

⇒ A - B = 60°

On solving the equations, we get A = 45° and B = - 15°.

Therefore, ∠A = 45°.

Some trigonometric ratios:

• sin 0° = 0
• sin 30° = 1/2
• cos 30° = √3/2
• sin 45° = 1/√2 [same as cos 45°]
• sin 90° = 1
• cos 90° = 0