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A+B = 5 pie/4, ( (1+cotA) ( 1 + cotB) )/(cotAcotB) = ?



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hartnn
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( (1+cotA) ( 1 + cotB) )/(cotAcotB)
= (1+cot A + cot B + cot A cot B) / cotA cot B
now separate the denominator.

Yahoo!
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tanAtanB + TanA + tanB + 1

hartnn
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what ?

hartnn
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= (1+cot A + cot B)/cotAcot B + (cot A cot B) / cotA cot B
= (1+cot A + cot B)/cotAcot B + 1

hartnn
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that '1' will be a trouble...

hartnn
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cot (A+B) =.... ?

hartnn
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ok, lets work with tan
tan(A+B) = tan 5pi/4 = ... ?

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tan 5pi/4=1

hartnn
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tan(A+B) = (tan A+tan B) /(1+tan A. tan B) = ...

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tan(A+B) = (tan A+tan B) /(1tan A. tan B)

hartnn
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oops,
tan(A+B) = (tan A+tan B) /(1tan A. tan B) =1
which gives
tan A+tan B = 1tan A tan B

hartnn
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so, tanAtanB + TanA + tanB + 1=...?

hartnn
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tanAtanB + TanA + tanB + 1= tanAtanB +1tan Atan B+ 1=2

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Yup... thxx...