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anonymous
 5 years ago
Show that cos(2x) = (1t^2)/(1+t^2) when t = tan x
anonymous
 5 years ago
Show that cos(2x) = (1t^2)/(1+t^2) when t = tan x

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0cos(2x) = cos^2x  sin^2x (1  tan^2x)/1 + tan^2x 1 + tan^2x = sec^2x (1tan^2x)/ sec^2x sec^2x = 1/cos^2x (1  tan^2x)/ 1/cos^2x divide by a fraction means * by reciprocal (1  tan^2x) * cos^2x distribute cos^2x  cos^2xtan^2x tan^2x = sin^2x/cos^2x cos^2x  cos^2x(sin^2x)/cos^2x cos^2x cancel cos^2x  sin^2x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0since the fractions here are rather complex, i may explain it to you by images, ok?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Above is the verification of the equation. Here is another way to prove it. By drawing the right triangle, if t = tanx, then sinx = t/[sqrt(1+t^2)] and cosx = 1/[sqrt(1+t^2)]. So cos(2x) = cos^(x)  sin^2(x) = 1/(1+t^2)  (t^2)/(1+t^2) = (1t^2)/(1+t^2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can you see the picture
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