SOLUTION: Prove: 1)sec^2x(1-sin^2x)=1 2)sinxcosxtanx=1-cos^2x 3)(cotx/cscx)=cosx 4)((1-cos^2/tanx))=sinxcosx 5)(tanx/secx)=sinx Can someone please help me by showing me the steps ??

Click here to see ALL problems on Trigonometry-basics

Question 268428: Prove:
1)sec^2x(1-sin^2x)=1
2)sinxcosxtanx=1-cos^2x
3)(cotx/cscx)=cosx
4)((1-cos^2/tanx))=sinxcosx
5)(tanx/secx)=sinx
Can someone please help me by showing me the steps ?? thank you:)
Answer by drk(1908) (Show Source):
You can put this solution on YOUR website!
1)sec^2x(1-sin^2x)=1
answer - -- >
Sec(x) = 1/cos(x)
1-sin^(x) = cos^2(x) so we get
(1/cos^2(x)) * (cos^2(x))
which is 1
1 = 1
-----
2)sinxcosxtanx=1-cos^2x
tan(x) = sin(x)/cos(x) so we get
sin(x)*cos(x)*sin(x)/cos(x)
this simplifies to
sin^2(x)
this is equal to
1 - cos^2(x) = 1-cos^2(x)
-----
3)(cotx/cscx)=cosx
cot(x) = cos(x) / sin(x)
csc(x) = 1/sin(x)
So we get
(cos(x) / sin(x)) / (1/sin(x))
which is
(cos(x) / sin(x))* (sin(x)/1)
or simply sin(x) = sin(x)
-----
4)((1-cos^2/tanx))=sinxcosx
1-cos^2(x) = sin^2(x)
tan(x) = sin(x) / cos(x)
so we get
(sin^2(x))/(sin(x) / cos(x))
and then
(sin^2(x))*(cos(x)/sin(x))
which is
sin(x)cos(x) = sin(x)cos(x)
-----
5)(tanx/secx)=sinx
tan(x) = sin(x)/cos(x)
sec(x) = 1/cos(x)
so we get
(sin(x)/cos(x))/ (1/cos(x))
simplify to get
(sin(x)/cos(x))* cos(x)/1
or just
sin(x) = sin(x)