I need urgent help solving a trig identity

[Antman059]

i cannot get this for the life of me and it is killing me, if someone can help it would be greatly appreciated:


i need to prove prove

csc^2 x - cos^2 x = cos^2 x + sin^4 x / sin^2 x

after the equal the slash represents a fraction

 

[stapel]

i need to prove prove

csc^2 x - cos^2 x = cos^2 x + sin^4 x / sin^2 x

after the equal the slash represents a fraction

Is the equation as follows?

. . . . .\(\displaystyle \csc^2(x)\, -\, \cos^2(x)\, =\, \cos^2(x)\, +\, \dfrac{\sin^4(x)}{\sin^2(x)}\)

What have you tried so far? Where are you stuck?

Please be complete. Thank you!

 

[Antman059]

no after the equal sign the cos is on the top half with the sin and i have tried converting csc to 1/sin

 

[ksdhart]

Assuming the equation is as follows:

\(\displaystyle \:csc^2x-cos^2x=\frac{cos^2x+sin^4x}{sin^2x}\)

I'd suggest you not bother with turning csc into 1/sin, but instead start with the right side. Break it apart into two separate fractions, like so:

\(\displaystyle \:csc^2x-cos^2x=\frac{cos^2x}{sin^2x}+\frac{sin^4x}{sin^2x}\)

After simplifying, you'll be left with a much simpler equation you should be able to prove easily.