Question

prove the identity
1+sin2x/sin2x=1+(1/2)secxcscx

Answer 1

\[\large \frac{1+\sin 2x}{\sin 2x}=1+\frac{1}{2}\sec x \cdot \csc x\]So let's work with the left side, and make it look like the right side. It shouldn't be too bad, we just have to apply some trig identities. Let's first split up the fraction on the left.\[\large \frac{1}{\sin 2x}+\frac{\sin 2x}{\sin 2x}\]

Answer 2

\[\large \frac{1}{\sin 2x}+1\]Understand that part ok? :)

Answer 3

yes

Answer 4

From here we'll want to apply the Double Angle Formula for Sine.\[\large \sin 2x=2 \sin x \cdot \cos x\]Applying this to our problem gives us,\[\large \frac{1}{\sin 2x}+1 \quad = \quad \frac{1}{2\sin x \cdot \cos x}+1\]

Answer 5

ok

Answer 6

From here, if you split up the multiplication of the first term, it might be a little easier to see what is going on.\[\large \frac{1}{2\sin x \cdot \cos x}+1 \quad = \quad \frac{1}{2}\cdot\frac{1}{\sin x}\cdot \frac{1}{\cos x}+1\]

Answer 7

Do you remember any more identities we can apply? :)

Answer 8

umm 1/cos= sec

Answer 9

1/sin/csc?

Answer 10

=csc*

Yayyyy team \c:/
That's pretty much it!

Answer 11

thank u:D