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標題:

有a.maths 唔識做

發問:

1) prove that con(A + B)COS(A-B) = cos^2 A - sin^2 B 2) prove that cot(A+B) = (cotAcotB-1) / (cotA + cotB)

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最佳解答:

1) cos(A + B)cos(A-B) =(cosAcosB - sinAsinB)(cosAcosB + sinAsinB) =(cosAcosB)^2 - (sinAsinB)^2 =(cos^2 A)(1- sin^2 B) - (sin^2 B)(1-cos^2 A) = cos^2 A - (cos^2 A)(sin^2 B) - sin^2 B + (cos^2 A)(sin^2 B) = cos^2 A - sin^2 B 2) cot(A+B) =1/tan(A+B) =1/[(tanA+tanB)/(1-tanAtanB)] =(1-tanAtanB)/(tanA+tanB) 分子分母各除以(tanAtanB) = (cotAcotB-1) / (cotA + cotB)

其他解答:

(1) LHS=cos(A+B)cos(A-B) =1/2(cos2A+cos2B) =1/2(2cos^2 A-1+1-2sin^2 B) =cos^2 A-sin^2 B =RHS (2) LHS=cot(A+B) =cos(A+B)/sin(A+B) =(cosAcosB-sinAsinB)/(sinAcosB+cosAsinB) =(cotAcotB-1)/(cotB+cotA) [Divided by sinAsinB on both sides] =RHS