Prove that cos^2(45º – a ) - sin^2 (45º – a) = sin2a

see explanation

Step-by-step explanation:

Using the addition identity for sine

sin(x + y) = sinxcosy - cosxsiny

Consider the left side

cos²(45 - A) - sin²(45 - A)

cos²(45 - A) = 1 - sin²(45 - A), thus

1 - sin²(45 - A) - sin²(45 - A)

= 1 - 2sin²(45 - A) ← expand sin(45 - A)

= 1 - 2(sin45cosA - cos45sinA)²

= 1 - 2(cosA - sinA)²

= 1 - 2(cos²A - sinAcosA + sin²A)

= 1 - cos²A + 2sinAcosA - sin²A

= sin²A + 2sinAcosA - sin²A

= 2sinAcosA

= sin2A = right side ⇒ verified

answer: a rhombus has two lines of symmetry that run through one vertex to the one directly across it. unlike a square, planes through the center of each edge of a rhombus do not yield mirrored sides.

step-by-step explanation:

24+x=y

step-by-step explanation: