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Exercise

sin(x+h)−sinxsin\left(x+h\right)-sinx

Step-by-step Solution

1

Using the sine of a sum formula: sin⁡(α±β)=sin⁡(α)cos⁡(β)±cos⁡(α)sin⁡(β)\sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta), where angle α\alpha equals xx, and angle β\beta equals hh

sin⁡(x)cos⁡(h)+cos⁡(x)sin⁡(h)−sin⁡(x)\sin\left(x\right)\cos\left(h\right)+\cos\left(x\right)\sin\left(h\right)-\sin\left(x\right)

Final answer to the exercise

sin⁡(x)cos⁡(h)+cos⁡(x)sin⁡(h)−sin⁡(x)\sin\left(x\right)\cos\left(h\right)+\cos\left(x\right)\sin\left(h\right)-\sin\left(x\right)

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  • Verify if true (using algebra)
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  • Product of Binomials with Common Term
  • FOIL Method
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sin(x+h)−sinx
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