# trigo question

• Aug 10th 2009, 06:58 AM
thereddevils
trigo question
$\displaystyle cosec\theta= cot\frac{\theta}{2}-cot \theta$

$\displaystyle cosec 2 \theta=cot \theta-cot 2 \theta$

$\displaystyle cosec 3 \theta = cot\frac{3 \theta}{2}- \cot 3 \theta$

I am not sure if the above is possible . Can i do that for the \theta above ? By just altering the theta like that ?
• Aug 10th 2009, 07:29 AM
skeeter
Quote:

Originally Posted by thereddevils
$\displaystyle cosec\theta= cot\frac{\theta}{2}-cot \theta$

$\displaystyle cosec 2 \theta=cot \theta-cot 2 \theta$

$\displaystyle cosec 3 \theta = cot\frac{3 \theta}{2}- \cot 3 \theta$

I am not sure if the above is possible . Can i do that for the \theta above ? By just altering the theta like that ?

It's just substitution.

Usually better form to use a different variable, like let $\displaystyle \theta = 2\alpha$ or $\displaystyle \theta = 3\beta$

$\displaystyle \csc{\theta}= \cot{\frac{\theta}{2}}-\cot{\theta}$

$\displaystyle \csc{2\alpha}= \cot{\alpha}-\cot{2\alpha}$

$\displaystyle \csc{3\beta}= \cot{\frac{3\beta}{2}}-\cot{3\beta}$