How do you simplify tan(x+y)-cos(x-y)tan(x+y)−cos(x−y) to trigonometric functions of x and y?

1 Answer
Shwetank Mauria
Jun 25, 2016

tan(x+y)-cos(x-y)=(tanx-tany)/(1-tanxtany)-cosxcosy-sinxsinytan(x+y)−cos(x−y)=tanx−tany1−tanxtany−cosxcosy−sinxsiny

Explanation:

We use the formulas

tan(A+B)=(tanA-tanB)/(1-tanAtanB)tan(A+B)=tanA−tanB1−tanAtanB and

cos(A-B)=cosAcosB+sinAsinBcos(A−B)=cosAcosB+sinAsinB

Hence tan(x+y)-cos(x-y)tan(x+y)−cos(x−y)

= (tanx-tany)/(1-tanxtany)-cosxcosy-sinxsinytanx−tany1−tanxtany−cosxcosy−sinxsiny

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