sin 2 + cos 2 = 1 α + β = 3 π 4 sin ⁡ ( α + β ) = 2 2 Why then cos ⁡ ( α + β ) = − 2 2 if sin 2 ⁡ ( x ) + cos 2 ⁡ ( x ) = 1I keep getting answer on calculator 2 2 Can someone please tell me what am I doing wrong?

Question

sin    2    +      cos    2    =  1  α  +  β  =            3      π        4    sin  ⁡  (  α  +  β  )  =            2        2  Why then   cos  ⁡  (  α  +  β  )  =  −            2        2   if       sin    2    ⁡  (  x  )  +      cos    2    ⁡  (  x  )  =  1I keep getting answer on calculator             2        2  Can someone please tell me what am I doing wrong?

Finnegan Stone · Accepted Answer

Square both.      sin    2    ⁡  (  α  +  β  )  =            (                        2                2            )        2    =      2    4    =      1    2        cos    2    ⁡  (  α  +  β  )  =            (                        −                      2                          2            )        2    =      2    4    =      1    2  So the sum of squares is 1 as required.

Why cos(alpha+beta)=−(sqrt(2))/(2) if sin^2(x)+cos^2(x)=1

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