Question

Verify that each equation is an identity: csc 2θ=1/2sec θ csc θ

Answer 1

So you're verifying the identity?

Answer 2

I'm verify that the equation is an identity

Answer 3

*verifying

Answer 4

Ok, so you're verifying the identity. Give me one moment to solve this, k?

Answer 5

okay, thank you very much!

Answer 6

Almost done

Answer 7

okay :)

Answer 8

Do you have your trig identities sheet?

Answer 9

yes

Answer 10

So the first thing you need to do here is change everything to sin and cos. You're going to do this to the right hand side because t is the most complex side. What does this equation look like after you've done that?

Answer 11

1/sin2 θ =1/2 1/cos θ 1/sin θ

Answer 12

Yup. So then you're going to multiply the right side all together

Answer 13

ohhh okay

Answer 14

So what's that going to look like?

Answer 15

1/sin2θ= 1/2 1/cos θsin θ

Answer 16

Don't change the left hand side. When you multiply it, it'll look like this:

\[\csc2\theta = \frac{ 1 }{ 2\cos \theta \sin \theta }\]

Answer 17

So then you're going to do
\[\csc2 \theta = \frac{ 1 }{ 2\sin \theta }\]

Answer 18

\[\csc2 \theta = \csc2 \theta\]

Answer 19

what happeneds to the cos θ?

Answer 20

There's a trig property that states that 2cosθsinθ is equal to 2sinθ, I substituted

Answer 21

oh yeah! thank you

Answer 22

You're welcome :)