If cos (α + β) = 0 then sin (α – β) = ?

Question

Philoid · Accepted Answer

We are given that: cos (α + β) = 0

∴We can rewrite it as: cos (α + β) = cos (90° – 0°)

On comparing both sides, we get,

(α + β) = 0 = 90°

⇒ α = 90° – β

Therefore, sin (α – β) = sin (90° – β – β)

= sin (90° – 2β)

= cos 2β