verify identity: (sin^2(x)) (csc^2(x) - 1) = cos^2(x)

[teener burns math]

Veriify the following identities by transforming the left side into the right side. Show every step for full credit.

. . .(sin^2(x)) (csc^2(x) - 1) = cos^2(x)

I can't do it. Help, please? Thank you!

 

[galactus]

Here's a hint:

\(\displaystyle \L\\csc^{2}(x)-1=cot^{2}(x)\)

Remember, \(\displaystyle \L\\\frac{sin(x)}{cos(x)}=tan(x)\)

 

[soroban]

Re: verifying identities...

Hello, teener burns math!

Veryify: \(\displaystyle \:\sin^2x(\csc^2x\,-\,1)\:=\:\cos^2x\)

On the left side, multiply: \(\displaystyle \:\underbrace{(\sin^2x)(\csc^2x)}\,-\,\sin^2x\)
. . . . . . . . . . . . . . . . . . . . . .\(\displaystyle = \;\underbrace{1\;-\;\sin^2x}\)
. . . . . . . . . . . . . . . . . . . . . . . . \(\displaystyle = \;\cos^2x\)