Question

Given that `sin (α - β) = 1/2` and `cos (α + β) = 1/2`, then α = ______ β = ______.

Answer 1

Given that `sin (α - β) = 1/2` and `cos (α + β) = 1/2`, then α = 45° β = 15°.

Explanation:

Let u = α − β and v = α + β.

Then `sin u = 1/2 ⇒ u = 30^circ`   ...(Principal value) 

And `cos v = 1/2 ⇒ v = 60^circ`   ...(Principal value)

Solve `α = (u + v)/2` 

= `(30^circ + 60^circ)/2`

= 45°

`β = (v - u)/2` 

= `(60^circ - 30^circ)/2`

= 15°