tan15°+tan75°

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tan15°+tan75°

tan15°+tan75°
tan15°+tan75°

tan15°+tan75°
方法一:
tan15°+tan75°
=tan(45°-30°)+tan(45°+30°)
=tan45°tan30°/(1+tan45°tan30°)+tan45°tan30°/(1-tan45°tan30°)
=4
方法二:
如楼上,将tan转化为sin/cos.但楼上计算有误.
方法三:
tan15°+tan75°
=tan15°+cot15°
=1/(sin15°cos15°)
=2/(2sin15°cos°)
=2/sin30°
=4
(证明:
tanx+cotx
=sinx/cosx+cosx/sinx
=(sin²x+cos²x)/(sinxcosx)
=1/(sinxcosx))

tan15+tan75
=sin15/cos15+sin75/cos75
=(sin15cos75+cos15sin75)/cos15cos75
=2sin(15+75)/[cos(15+75)/2+cos(15-75)/2]
=2sin90/[cos45+cos30]
=4/(√2+√3)
=4(√3-√2)