trig identitys

**andrewpark2** · November 26th 2008, 05:11 PM

Prove these identitys

sinO/1+cosO=1-cosO/sinO

1-tanO= -tanO(1-1/tanO)

**skeeter** · November 26th 2008, 05:26 PM

Originally Posted by andrewpark2

Prove these identitys

sinO/1+cosO=1-cosO/sinO

1-tanO= -tanO(1-1/tanO)

for the first one, multiply the left side by $\frac{1 - \cos{O}}{1 - \cos{O}}$
note that $1 - \cos^2{O} = \sin^2{O}$

for the second one, just distribute the right side

**great_math** · November 26th 2008, 06:49 PM

Originally Posted by andrewpark2

Prove these identitys

1-tanO= -tan O(1-1/tan O)

$<br /> 1-\tan O=-\tan O\left(1- \frac 1{\tan O}\right)$

Consider RHS $-\tan O\left(1- \frac 1{\tan O}\right)$

$\implies \tan O\left(\frac 1{\tan O}-1\right)$

$\implies \tan O\left(\frac {1-\tan O}{\tan O}\right)$

$\implies 1-\tan O=LHS$

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