Addition formulae

quader

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Use the addition formulae to find an expression for cos²(A+B)+sin²(A+B). Verify that your expression reduces to 1.

Use a similar method to find an expression for cos²(A+B)-sin²(A+B). Verify that this reduces to cos(2A + 2B)


So I get the the stage: cos²A(cos²B + sin²B) + sin²A(-sin²B + cos²B) = cos²A + sin²A(-sin²B + cos²B).
What can I do with the 'sin²A(-sin²B + cos²B)'? I can make it 'sin²A(2cos²B - 1)', but how would that help?
Please help
 
Use the addition formulae to find an expression for cos²(A+B)+sin²(A+B). Verify that your expression reduces to 1.

Use a similar method to find an expression for cos²(A+B)-sin²(A+B). Verify that this reduces to cos(2A + 2B)


So I get the the stage: cos²A(cos²B + sin²B) + sin²A(-sin²B + cos²B) = cos²A + sin²A(-sin²B + cos²B).
What can I do with the 'sin²A(-sin²B + cos²B)'? I can make it 'sin²A(2cos²B - 1)', but how would that help?
Please help

Check your signs. Your second term should not have a negative sign next to sin²B.
 
Use the addition formulae to find an expression for cos²(A+B)+sin²(A+B). Verify that your expression reduces to 1.

Frankly, I can see nothing there that needs verification.

\(\displaystyle \cos^2(LXXIV)+\sin^2(LXXIV)=1\) regardless of what LXXIV may mean as long as it is a number.
 
Yes, you have a negative so that when you add \(\displaystyle sin^2(A+ B)\) that term will cancel!
 
Sorry, I'm down to 'Cos²A + Sin²A(Cos²B - Sin²B)'.

I don't know what you mean by add Sin²(A+B)
 
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