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

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5

not sure but it may be b, as i said i'm not sure.