use a sum or difference formula to find the exact value of the trigonometric fun

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Mar 3rd, 2015

tan 15° = tan(π/12)

tan(π/3 − π/4)

= [tan(π/3) − tan(π/4)] / [1 + tan(π/3) tan(π/4)]

= [(√3)− 1] / [1 + (√3)×1]

= [(√3)− 1] / [(√3) + 1]

= [(√3)− 1]² / [(√3) + 1]×[(√3) − 1]

= [3 − 2(√3) + 1] / [3 − 1]

= [4 − 2(√3)] / 2

= 2 − √3


Mar 3rd, 2015

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