求证tan37.5°=根号6+根号3-根号2-2

要過程

tan37.5°=tan75°/2=(1-cos75°)/sin75°=[1-cos(45°+30°)]/sin(45°+30°)

=(1-cos45°cos30°+sin45°sin30°)/(sin45°cos30°+cos45°sin30°)

=(1-√2/2*√3/2+√2/2*1/2)/(√2/2*√3/2+√2/2*1/2)

=(1-√6/4+√2/4)/(√6/4+√2/4)

=[(4+√2-√6)/4]/[(√6+√2)/4]

=(4+√2-√6)/(√6+√2)

=(4√6+2√3-6-4√2-2+2√3)/4

=(4√6+4√3-4√2-8)/4

=√6+√3-√2-2

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