Question

prove the above question and i will give you....​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos²A - sin²B = cos(A + B) . cos(A - B)

Here A = $\frac{\pi }{8}$ + $\frac{A}{2}$ , B = $\frac{\pi }{8}$ - $\frac{A}{2}$

Consider the left side

cos²($\frac{\pi }{8}$ + $\frac{A}{2}$ ) - sin²( $\frac{\pi }{8}$ - $\frac{A}{2}$ )

= cos($\frac{\pi }{8}$ + $\frac{A}{2}$ + $\frac{\pi }{8}$ - $\frac{A}{2}$ ) × cos($\frac{\pi }{8}$ + $\frac{A}{2}$ - $\frac{\pi }{8}$ + $\frac{A}{2}$ )

= cos ($\frac{\pi }{4}$ ) × cos ( A)

= $\frac{1}{\sqrt{2} }$ cosA

=  right side , thus proven