Question

Please help me!!!!!​ i need full answer.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the sum/ difference → product formula

cos x - cos y = - 2sin( $\frac{x+y}{2}$)sin ($\frac{x-y}{2}$ )

sin x - sin y = 2cos ($\frac{x+y}{2}$ )sin ($\frac{x-y}{2}$ )

Given

(cosA - cosB)² + (sinA - sinB )²

= [ - 2sin($\frac{A+B}{2}$)sin($\frac{A-B}{2}$ ) ]² + [ 2cos($\frac{A+B}{2}$ )sin($\frac{A-B}{2}$ ) ]²

= 4sin² ($\frac{A+B}{2}$ )sin² ($\frac{A-B}{2}$ ) + 4cos² ($\frac{A+B}{2}$ )sin² ( $\frac{A-B}{2}$ )

= 4sin² ($\frac{A-B}{2}$ )[ sin² ( $\frac{A+B}{2}$ ) + cos² ( $\frac{A+B}{2}$ ) ← sin²x + cos²x = 1

= 4sin² ( $\frac{A-B}{2}$ ) × 1

= 4sin² ( $\frac{A-B}{2}$ ) = right side ⇒ proven