64.3k views
1 vote
How to verify with steps?

How to verify with steps?-example-1
User PratZ
by
8.9k points

1 Answer

5 votes


csc(-x)-1~~ = ~~\cfrac{cos^2(x)}{csc(-x)+1} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{cos^2(x)}{csc(-x)+1}\implies \cfrac{1-sin^2(x)}{(1)/(sin(-x)+1)}\implies \cfrac{1-sin^2(x)}{(1)/(-sin(x)+1)}\implies \cfrac{[1-sin(x)][1+sin(x)]}{ ~~ (-1+sin(x))/(sin(x)) ~~ } \\\\\\\ [1-sin(x)][1+sin(x)]\cdot \cfrac{sin(x)}{-1+sin(x)} \\\\\\\ [1-sin(x)][1+sin(x)]\cdot \cfrac{sin(x)}{-[1-sin(x)]} \\\\\\\ [1+sin(x)][-sin(x)] \implies \boxed{-sin(x)-sin^2(x)} \\\\[-0.35em] ~\dotfill


csc(-x)-1\implies \cfrac{1}{sin(-x)}-1\implies \cfrac{1}{-sin(x)}-1\implies \boxed{\cfrac{-1-sin(x)}{sin(x)}}

now, as you can see is a no dice, before doing many simplifications, I often check them graphically, so I know what's cooking, anyhow, Check the picture below, they are definitely not the same, the red one is the one on the right-hand-side.

How to verify with steps?-example-1
User Hard
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories