# Thread: Verifing Idnetities Help

1. ## Verifing Idnetities Help

I'm currently trying to verify these three identities and they are giving me some trouble.
They are:
1.(sin^2x-2sin^4x+sin^6x)=sin^2xcos^4x
2. secx+cscx/1+tanx=cscx
3. cosx-(cosx/1-tanx)=sinxcosx/sinx-cosx

2. Originally Posted by Ciccone07
I'm currently trying to verify these three identities and they are giving me some trouble.
They are:
1.(sin^2x-2sin^4x+sin^6x)=sin^2xcos^4x

$\sin^2x-2\sin^4x+\sin^6x=\sin^2x(1-2\sin^2x+\sin^4x)=\sin^2x(1-\sin^2x)^2=\sin^2x\cos^4x$ , using $\cos^2x+\sin^2x=1$ .

Now you play as above with the other identities...

Tonio

2. secx+cscx/1+tanx=cscx
3. cosx-(cosx/1-tanx)=sinxcosx/sinx-cosx

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3. ## Trig Identies

Originally Posted by Ciccone07
I'm currently trying to verify these three identities and they are giving me some trouble.
They are:
1.(sin^2x-2sin^4x+sin^6x)=sin^2xcos^4x
2. secx+cscx/1+tanx=cscx
3. cosx-(cosx/1-tanx)=sinxcosx/sinx-cosx
I'm currently trying to verify these three identities and they are giving me some trouble.
They are:
1.(sin^2x-2sin^4x+sin^6x)=sin^2xcos^4x

(sin(x))^2 (cos(x))^4
= (sin(x))^2 ( 1 - sin(x))^2 )^2
= (sin(x))^2 ( 1 - 2 (sin(x))^2 + (sin(x))^4 )
= (sin(x))^2 - 2 (sin(x))^4 + (sin(x))^6

2. secx+cscx/1+tanx=cscx

(sec(x) + csc(x)) / ( 1 + tan(x))
= (1/cos(x) + (1/sin(x) ) / (1 + sin(x)/(cos(x) )
= (1 + cos(x)/sin(x) )/(cos(x) + sin(x) )
= (1/sin(x) ) ( sin(x) + cos(x) )/(cos(x) + sin(x))
= 1/sin(x)
= csc(x)

3. cosx-(cosx/1-tanx)=sinxcosx/sinx-cosx

( cos(x) (1 - tan(x) ) - cos(x) )/ (1 - tan(x))
= (cos(x) - cos(x) tan(x) - cos(x) )/( 1 - tan(x))
= - cos(x) tan(x) / ( 1 - tan(x))
= - sin(x) / (1 - tan(x))
= - sin(x) cos(x) / ( cos(x) - sin(x))

= cos(x) sin(x) / (sin(x) - cos(x))

Kermit