Prove this identity: sin^2(x + 45) + cos^2(x - 45)

[hndalama]

Prove this identity: sin^2(x + 45) + cos^2(x - 45) = 1 + 2sinxcosx

sin²(x + 45) + cos²(x - 45) = 1 + 2sinxcosx

my attempt is as follows:

sin(x + 45)² + cos(x - 45)²
(root2/2 *sinx + root2/2 *cosx)² + (root2/2 *cosx + root2/2 *sinx)²
(sin²x +cos²x + 2sinxcosx) + (sin²x +cos²x + 2sinxcosx)
2 + 4sinxcosx

 

[Deleted member 4993]

sin²(x + 45) + cos²(x - 45)

my attempt is as follows:

I do not see an identity.

Please review your post - edit it and repost.

 

[hndalama]

I do not see an identity.

Please review your post - edit it and repost.

Thank you, I have edited the post

 

[Deleted member 4993]

sin²(x + 45) + cos²(x - 45) = 1 + 2sinxcosx

my attempt is as follows:

sin(x + 45)² + cos(x - 45)²

(root2/2 *sinx + root2/2 *cosx)² + (root2/2 *cosx + root2/2 *sinx)²

(sin²x +cos²x + 2sinxcosx) + (sin²x +cos²x + 2sinxcosx)

2 + 4sinxcosx

sin(x + 45)² + cos(x - 45)²

(root2/2 *sinx + root2/2 *cosx)² + (root2/2 *cosx + root2/2 *sinx)²

[√2/2]² {(sin²x +cos²x + 2sinxcosx) + (sin²x +cos²x + 2sinxcosx)}
[1/2]{2 + 4sinxcosx}

and continue....

 

[hndalama]

and continue....

Oh silly me! Thanks for showing me my mistake.
Can you also show me how you typed the root symbol "[√2/2] " ?