1) Use the compound angle formula for Sin(A+B) = sinAcosB + cosAsinB and sin((π/2)-A) = cosA to derive the formula for cos (A-B)
2) Express tan(A + B + C) in terms of tanA, tanB and tanC.
Please show ur steps.
[20分]兩條Trigonometric Relation question
2007-07-10 5:16 am
回答 (1)
2007-07-10 5:31 am
✔ 最佳答案
cos(A-B)= sin( π/2-(A-B) )
= sin(π/2 - A + B)
= sin(π/2 - A)cosB + cos(π/2 - A)sinB
= cosAcosB + sin( π/2 - (π/2 - A) )sinB
= cosAcosB + sinAsinB
tan(A + B + C)
= [ tan(A + B) + tanC ] / [ 1 - tan(A + B)tanC ]
= [ (tanA + tanB) / (1 - tanAtanB) + tanC ] / [ 1 - (tanA + tanB)tanC / (1 - tanAtanB) ]
= [ (tanA + tanB) + (1 - tanAtanB)tanC ] / [ (1 - tanAtanB) - (tanA + tanB)tanC ]
= (tanA + tanB + tanC - tanAtanBtanC) / (1 - tanAtanB - tanAtanC - tanBtanC)
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