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证明：tanα/2-1/（tanα/2）=-2/tanα还有.tan(x/2+π/4）+tan(x/2-π/4）=2tanx
题目详情
证明：tanα/2-1/（tanα/2）=-2/tanα
还有.tan(x/2+π/4）+tan(x/2-π/4）=2tanx
还有.tan(x/2+π/4）+tan(x/2-π/4）=2tanx
▼优质解答
答案和解析
1.tan(a/2)-1/tan(a/2)=[(tan(a/2)^2-1]/tan(a/2)
tana=2tan(a/2)/[1-tan(a/2)^2] -2/tana=[(tan(a/2)^2-1]/tan(a/2)
所以tanα/2-1/（tanα/2）=-2/tanα即得证
2.tan(x/2+π/4）+tan(x/2-π/4）=2tanx
[tan(x/2)+1]/[1-tan(x/2)]+[tan(x/2)-1]/[1+tan(x/2)]
=[tan(x/2)+1]^2-[(tanx/2)-1]^2/[1-tan^2(x/2)]
=4tan(x/2)/[1-tan^2(x/2)]=2tanx
tana=2tan(a/2)/[1-tan(a/2)^2] -2/tana=[(tan(a/2)^2-1]/tan(a/2)
所以tanα/2-1/（tanα/2）=-2/tanα即得证
2.tan(x/2+π/4）+tan(x/2-π/4）=2tanx
[tan(x/2)+1]/[1-tan(x/2)]+[tan(x/2)-1]/[1+tan(x/2)]
=[tan(x/2)+1]^2-[(tanx/2)-1]^2/[1-tan^2(x/2)]
=4tan(x/2)/[1-tan^2(x/2)]=2tanx
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