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cot(45°+x)=2则(1+sec2x-tan2x)/(1+sec2x+tan2x)=
题目详情
cot(45°+ x)=2
则(1+sec2x-tan2x)/(1+sec2x+tan2x)=
则(1+sec2x-tan2x)/(1+sec2x+tan2x)=
▼优质解答
答案和解析
tan(45°+ x)=1/2
(1+sec2x-tan2x)/(1+sec2x+tan2x)=
[1+1/cos2x-tan2x]/[1+1/cos2x+tan2x]
上下同时乘以cos2x
=[cos2x-sin2x+1]/[cos2x+1+sin2x]
=[2cosx^2-1+1-2sinxcosx]/[2cos^2-1+1+2sinxcosx]
=(cosx^2-sinxcosx)/(cos^2+sinxcosx)
=(1-tanx)/(1+tanx)
=2
(1+sec2x-tan2x)/(1+sec2x+tan2x)=
[1+1/cos2x-tan2x]/[1+1/cos2x+tan2x]
上下同时乘以cos2x
=[cos2x-sin2x+1]/[cos2x+1+sin2x]
=[2cosx^2-1+1-2sinxcosx]/[2cos^2-1+1+2sinxcosx]
=(cosx^2-sinxcosx)/(cos^2+sinxcosx)
=(1-tanx)/(1+tanx)
=2
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