1. ## Proving the identity

I just started A-level maths and I couldn’t able to do this maths question.
Prove the identity
1/(cosecx-1) - 1/(cosecx+1) = 2(tan^2)x

2. $L.H.S. = \frac{1}{csc(x)-1} - \frac{1}{csc(x)+1} = \frac{csc(x)+1-(csc(x)-1)}{(csc(x)-1)(csc(x)+1}$

now simplify and complete!!

Note: $csc^{2}(x) - cot^{2}(x) = 1$

3. Originally Posted by harish21
$L.H.S. = \frac{1}{csc(x)-1} - \frac{1}{csc(x)+1} = \frac{csc(x)+1-(csc(x)-1)}{(csc(x)-1)(csc(x)+1}$

now simplify and complete!!

Note: $csc^{2}(x) - cot^{2}(x) = 1$
ok this is what i have after simplifying.

2/(cosecx-1)

i am not sure if i am correct or not and What do i do next?

4. NOOOO....

$\frac{csc(x)+1-(csc(x)-1)}{(csc(x)-1)(csc(x)+1}= \frac{2}{csc^{2}(x)-1} = \frac{2}{cot^{2}(x)} = 2 \times \frac{1}{cot^{2}(x)} = 2tan^{2}(x)$

Remember that:

$(csc(x)-1)(csc(x)+1) = csc^{2}(x)-1$ BECAUSE $(a-b)(a+b) = a^2-b^2$

Hope this helps..
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