Establish identitiy ( cos ⁡ θ − sin ⁡ θ ) 2 + ( cos ⁡ θ + sin ⁡ θ ) 2 = 2

Question

Establish identitiy   (  cos  ⁡  θ  −  sin  ⁡  θ      )    2    +  (  cos  ⁡  θ  +  sin  ⁡  θ      )    2    =  2

alisonhleel3 · Accepted Answer

Set:   a  =  cos  ⁡  θ,   b  =  sin  ⁡  θ. Then:  (  a  −  b      )    2    +  (  a  +  b      )    2    =      a    2    −  2  a  b  +      b    2    +      a    2    +  2  a  b  +      b    2    =  2      a    2    +  2      b    2    =  2  (      a    2    +      b    2    )  =  2  (  sin  ⁡      θ    2    +  cos  ⁡      θ    2    )  =  2.

Leah Pope · Accepted Answer

hint:   (  a  −  b      )    2    =      a    2    −  2  a  b  +      b    2    ,  (  a  +  b      )    2    =      a    2    +  2  a  b  +      b    2  , and       sin    2    ⁡  θ  +      cos    2    ⁡  θ  =  1. Use the above formulas with   a  =  sin  ⁡  θ  ,  b  =  cos  ⁡  θ

Establish identitiy ( cos ⁡ θ −

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