Help with manipulation please (1 Viewer)

MONKEYjulz

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hey, this might be a very easy question, but i've never encountered it before.

How does: inverse tan (2) - inverse tan (1/2) = inverse tan (3/4)

Help is appreciated, thanks
 

Asubmarine

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How does: inverse tan (2) - inverse tan (1/2) = inverse tan (3/4)
let inv. tan(2) = @ , inv. tan (1/2) = X and inv. tan (3/4) = Y
ie. (@-X)=Y
if (@-X)=Y then
tan(@-X) = tan(Y)

tan(@-X)= (tan@-tanX)/1+tan@tanX)

by defintion tan(@)=2 , tan(X)=1/2 and tan(Y)=3/4

so tan(@-X) = (2-0.5)/(1+2x0.5)
=1.5/2
=3/4
=tan(Y)

therefore (@-X)=Y
 

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