If cos (α + β) = 0 then sin (α

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

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

cos 2β

sin α

cos β

sin 2α

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cos (α + β) = 0 ⇒ α + β = 90º ⇒ α = 90º – β

$∴$ (α – β) = (90º – 2β) ⇒ sin (α – β) = sin (90º – 2β) = cos 2β.