Verify the identity (sinx + sin2x)/(1+cosx + cos2x)= tan x Please show step by step instructions
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Luca B.
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You should use the double angle formulas such that:
`sin 2x = 2 sin x cos x`
`cos 2x = 2cos^2 x - 1`
Hence, substituting `2 sin x cos x` for `sin 2x` and `2cos^2 x - 1` for `cos 2x` yields:
`(sinx + 2 sin x cos x)/(1+ cosx + 2cos^2 x - 1)= tan x`
You need to factor out sin x to numerator and cos x to denominator such that:
`(sin x(1 + 2 cos x))/(cos x(1 + 2 cos x)) = tan x`
Reducing `by 1+ 2 cos x` yields:
`sin x/cos x = tan x => tan x = tan x`
Hence, using the double angle formulas, yields that the given identity `(sinx + sin2x)/(1+cosx + cos2x)= tan x` holds.
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