Q:

prove that cos^2(45º – A ) - sin^2 (45º – A) = Sin2A

Accepted Solution

A:
Answer:see explanationStep-by-step explanation:Using the addition identity for sinesin(x + y) = sinxcosy - cosxsinyConsider the left sidecos²(45 - A) - sin²(45 - A)cos²(45 - A) = 1 - sin²(45 - A), thus1 - sin²(45 - A) - sin²(45 - A)= 1 - 2sin²(45 - A) ← expand sin(45 - A)= 1 - 2(sin45cosA - cos45sinA)²= 1 - 2([tex]\frac{\sqrt{2} }{2}[/tex]cosA - [tex]\frac{\sqrt{2} }{2}[/tex]sinA)²= 1 - 2([tex]\frac{1}{2}[/tex]cos²A - sinAcosA + [tex]\frac{1}{2}[/tex]sin²A)= 1 - cos²A + 2sinAcosA - sin²A= sin²A + 2sinAcosA - sin²A= 2sinAcosA= sin2A = right side ⇒ verified