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