Question

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

Answer 1

see explanation

Explanation:

Using the identity

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

Here A =
`(\pi )/(8)` +
`(A)/(2)` , B =
`(\pi )/(8)` -
`(A)/(2)`

Consider the left side

cos²(
`(\pi )/(8)` +
`(A)/(2)` ) - sin²(
`(\pi )/(8)` -
`(A)/(2)` )

= cos(
`(\pi )/(8)` +
`(A)/(2)` +
`(\pi )/(8)` -
`(A)/(2)` ) × cos(
`(\pi )/(8)` +
`(A)/(2)` -
`(\pi )/(8)` +
`(A)/(2)` )

= cos (
`(\pi )/(4)` ) × cos ( A)

=
`(1)/(√(2) )` cosA

= right side , thus proven