Originally Posted by

**kodx** I'm currently learning trigonometric identities and my favourite way of verifying a given trigonometric identity is to transform one side to the other.

I usually do this by reducing the terms of the side am working on down to sines and cosines and then manipulating them with algebra and the

basic trigonometric identities. I love this method because it makes it so clear to see how both sides are equivalent that even if I can prove an

identity some other way I still use this.

But am having trouble using this method on trigonometric identities expressed as fractions with more than 1 term in the denominator.

For example, could someone show me how one would go about employing this method to verify the following by transforming the left hand side to the right hand side?

$\displaystyle \frac{tan\: \beta}{1 - cot\: \beta} + \frac{cot\: \beta}{1 - tan\: \beta} = tan\: \beta + cot\: \beta + 1$