三角证明题
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RHS=secx-tanx/cosecx-cotx =1/cosx-sin²x/cosx-cosx/sinx =(sinx-sin³x-cos²x)/sinxcosx =(cosecx-sinx-cot²x)/cotx (Divide sin²x on both denominator and nominator) =cosecx+cos²x/sinx+tanx =cosecx+cotx/secx+tanx =LHS
考虑 (csc x + cot x/sec x + tan x) - (sec x- tan x/csc x - cot x) =1/sin x + (cos x/sin x)(1/cos x) + sin x/cos x - 1/cos x + (sin x/cos x)(1/sin x) + cos x/sin x =1/sin x + 1/sin x + sin x/cos x - 1/cos x + 1/cos x + cos x/sin x =2/sin x + sin x/cos x + cos x/sin x =2/sin x + 1/(sin x)(cos x) 不等于0
考虑 (csc x + cot x/sec x + tan x) - (sec x- tan x/csc x - cot x) =1/sin x + (cos x/sin x)(1/cos x) + sin x/cos x - 1/cos x + (sin x/cos x)(1/sin x) + cos x/sin x =1/sin x + 1/sin x + sin x/cos x - 1/cos x + 1/cos x + cos x/sin x =2/sin x + sin x/cos x + cos x/sin x =2/sin x + 1/(sin x)(cos x) 不等于0
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