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Please solve! Further Trig Question From New Senior Mathematics (1 Viewer)

Thread starter chris_power_96
Start date Jul 26, 2012

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chris_power_96

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#1

Prove: (2cos(x/2)-1-cosx)/(<meta charset="utf-8">2cos(x/2)+1+cosx)=(1-cos(x/2))/(1+cos(x/2))

Sy123

This too shall pass

#2

$LHS=\frac{2\cos\frac{x}{2}-1-\cos x}{2\cos \frac{x}{2}+1+\cos x} \\ \\ \cos x=2\cos^2 \frac{x}{2}-1 \\ \\ LHS=\frac{2\cos0.5x-1-2\cos^20.5x+1}{2\cos0.5x+1+2\cos^20.5x-1}=\frac{2\cos 0.5x(1-\cos 0.5x)}{2\cos 0.5x(1+\cos0.5x)}=\frac{1-\cos \frac{x}{2}}{1+\cos \frac{x}{2}} \\ =RHS \\ \\ \square$

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