How do you prove: -2= (cot^2θ/1+cscθ) + (cot^2θ/1-cscθ)

Question

How do I prove that both sides are the same?? I can't figure it out

Answer 1

Greetings! Lets solve this shall we ?

So, we must simplify this equation to confirm the left side of -2 such that

(cot²θ / [1+cscθ]) + (cot²θ / [1-cscθ]) = -2............We first find the common denominator to be (1+cscθ)(1-cscθ) such that

[cot²θ(1-cscθ) + cot²θ(1+cscθ)] / (1-csc²θ) = -2..........We distribute the cot²θ inside the numerators such that

[cot²θ - cscθcot²θ + cot²θ + cscθcot²θ] / (-cot²θ) = -2........Because -cot²θ = 1 - csc²θ and cancel out what needs to be cancelled such that

2cot²θ / (-cot²θ) = -2...............The cot²θ cancels out to confirm

-2 = -2

I hope this helped!