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More Trig Identities?

Britt :) - 2009-05-06 03:43:50 - Mathematics

Missing a week of school and being expected to know how to do Trig Identities blows. :( Could you please help me with these questions 1. [1+cotBtanx]/[(sin(B+x))/(sinBcosx)] 2. tan4x = [4tanx(1-tan^2x)]/[1-6tan^2x+tan^4x]

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1. sin(B+x) = sin B cos x + cos B sin x so sin (B+x) / (sin B cos x) = 1 + (cos B sin x) / (sin B cos x) = 1 + (cos B / sin B) (sin x / cos x) = 1 + cot B tan x So the whole expression = 1 2. Use tan(a+b) = (tan a + tan b) / (1 - tan a tan b) tan 4x = 2 tan 2x / ( 1 - tan^2 2x) = [ 4 tan x / (1 - tan^2 x) ] / [ 1 - 4 tan^2 x / ( 1 - tan^2x)^2 ] Multiply top and bottom by (1 - tan^2 x)^2 = [ 4 tan x ( 1 - tan^2 x) ] / [ (1 - tan^2 x)^2 - 4 tan^2 x ] = [ 4 tan x ( 1 - tan^2 x) ] / [ 1 - 2 tan^2 x + tan^4 x - 4 tan^2 x] = 4 tan x ( 1 - tan^2 x) / [ 1 - 6 tan^2 x + tan^4 x]