Prove that: cos^2 (45+A)+cos^2 (45-A)=1​

see explanation

Step-by-step explanation:

Using the cosine addition formula

cos(A ± B ) = cosAcosB ∓ sinAsinB

Then considering the left side

cos²(45 + A) + cos²(45 - A)

= [ cos45cosA - sin45sinA ]² + [cos45cosA + sin45sinA]]²

= [ cosA - sinA ]² + [ cosA + sinA ]²

= cos²A - sinAcosA + sin²A + cos²A + sinAcosA + sin²A

= cos²A + sin²A

= 1

= right side , then proven

Step-by-step explanation:

cos 2x=cos²x-sin²x=cos²x-(1-cos²x)=cos²x-1+cos²x=2cos²x-1

2cos²x=1+cos2x

cos²(45+A)+cos²(45-A)

cos (90-x)=sin x

cos (90+x)=-sin x

4th option is correct xy=-10

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