Question

Decide whether the equation is a trigonometric identitiy. Explain your reasoning

sin^2theta csc^2theta =sin^2theta +cos^2theta

Answer 1

I would, first, write everything in terms of \(\large sin\) and \(\large cos\)

Answer 2

and how would i do that haha I'm completely lost sorry

Answer 3

Don't worry about it lol

Well we have

\[\large sin^2\theta \times csc^2\theta = sin^2\theta + cos^2\theta\]

We want to have EVERYTHING be in terms of sin and cos...so if I tell you that

\[\large csc^2\theta = \frac{1}{sin^2\theta}\]

We would have

\[\large sin^2\theta \times \frac{1}{sin^2\theta} = sin^2\theta + cos^2\theta\]

And what would be next?

Answer 4

You can cancel Sin^2theta and 1/sin^2theta ?

Answer 5

Exactly

\[\large \frac{sin^2\theta}{sin^2\theta} = sin^2\theta + cos^2\theta\]

Meaning

\[\large 1 = sin^2\theta + cos^2\theta\]

And on the right side...what do we know about \(\large sin^2\theta + cos^2\theta\) ?

Answer 6

do they equal one?

Answer 7

Lol yes they do, that is one of the FIRST identities to know is \(\large sin^2x + cos^2x = 1\)

So we have \(\large 1 = 1\) and therefor we have proven it is an identity

Answer 8

thank you so much haha as you can tell I'm falling behind in class

Answer 9

Ehh it happens, just don't try and rush into whats going on NOW...make sure you understand these basics first :)