Question 41424: find the exact value of tan 15 degrees WITHOUT USING TABLES OR A CALCULATOR. be sure to show your work.
Answer by zeynep(43)   (Show Source):
You can put this solution on YOUR website! you can either draw a triangle of 15-75-90 degrees and show on it, or use
tan(a-b) formula.
I will use the second approach.
tan(a-b)=(tana-tanb)/(1+tana.tanb)
tan15=tan(60-45)=(tan60-tan45)/(1+tan60.tan45)=(sqrt3-1)/(1+sqrt3.1)
=(sqrt3-1)/(1+sqrt3) (now to make the denominator a rational number, we will multiply it with its conjugate;
=(sqrt3-1)(sqrt3-1)/(1+sqrt3)(sqrt3-1)=(sqrt3-1)^2/2
I hope it helps; I would have loved to solve by drawing the triangle, too however I do not know how to draw it here.If there is something you cannot understand, let me know!
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