Prove that

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- August 20th 2010, 06:40 AMPunchProving (Q8B)
Prove that

- August 20th 2010, 06:56 AMmathaddict
- August 20th 2010, 09:14 AMdevdel
2 sin(2x) = 4 sin(x)·cos(x)

sin(4x) = 2 sin(2x)·cos(2x) = 4sin(x)·cos(x)·cos(2x)

cos(2x) = cos(x)-sin(x)

→

Ok, with that solved we can now begin.

(2 sin(2x)-sin(4x))/(2sin(2x)+sin(4x)) =

(4sin(x)·cos(x)-4sin(x)·cos(x)·cos(2x))/(4(sin(x)·cos(x)+4sin(x)·cos(x)·cos(2x) =

(4sin(x)·cos(x)(1-cos(2x)))/(4sin(x)·cos(x)(1+cos(2x)) =

(1-cos(2x))/(1+cos(2x)) =

(1-(cos(x)-sin(x))/(1+cos(x)-sin(x)) =

(sin(x)+cos(x)-cos(x)+sin(x))/(sin(x)+cos(x)+cos(x)-sin(x) =

2sin(x)/2cos(x) = tan(x)