What formula or rule has been used here?I was in between proving a trigonometric identity but couldn't succeed. I went through the solution and saw this in between cos ⁡ A cos ⁡ B sin ⁡ A sin ⁡ B = 3 1 cos ⁡ A cos ⁡ B + sin ⁡ A sin ⁡ B cos ⁡ A cos ⁡ B − sin ⁡ A sin ⁡ B = 3 + 1 3 − 1 What happened there in the second step?

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What formula or rule has been used here?I was in between proving a trigonometric identity but couldn&#039;t succeed. I went through the solution and saw this in between                                          cos            ⁡            A            cos            ⁡            B                                sin            ⁡            A            sin            ⁡            B                                              =                  3          1                                                                        cos            ⁡            A            cos            ⁡            B            +            sin            ⁡            A            sin            ⁡            B                                cos            ⁡            A            cos            ⁡            B            −            sin            ⁡            A            sin            ⁡            B                                              =                              3            +            1                                3            −            1                              What happened there in the second step?

Abril Orr · Accepted Answer

If we have      x    y    =      3    1  then this means, by definition of fractions, that   x  =  3  y. This yields            x      +      y              x      −      y        =            3      y      +      y              3      y      −      y        =            3      +      1              3      −      1      In your case,   x  =  cos  ⁡  A  cos  ⁡  B and   y  =  sin  ⁡  A  sin  ⁡  B

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