Posted by suzi on .
1) 1+cos(3t)/ sin(3t) + sin(3t)/( 1+ cos(3t))= 2csc(3t)
2) sec^2 2u1/ sec^2 2u= sin^2 2u
3) cosB/1 sinB= secB+ tanB

Math Help 
Reiny,
Please type your equations using brackets to show the proper order of operation.
The way you typed them, none are identities.
e.g.
for the last one you probably meant:
cosB/(1sinB) = secB + tanB
then:
RS = 1/cosB + sinB/cosB
= = (1sinB)/cosB * (1+sinB)/(1+sinB)
= (1  sin^2 B)/(cosB(1+sinB)
= cos^2B/(cosB(1+sinB))
= cosB/(1+sinB)
= LS 
Math Help 
suzi,
1)1+cos(3t)/ sin(3t) + sin(3t)/( 1+ cos(3t))= 2csc(3t)
2)sec^2 (2u1)/ sec^2 (2u)= sin^2 (2u) 
Math Help 
Reiny,
in 1) since all angles are 3t, I will let x = 3t for easier typing
Again, the way you typed it, it does not work.
You must have meant
(1+cosx)/sinx + sinx/(1+cosx) = 2cscx
LS = ((1+cosx)^2 + sin^2x)/(sinx(1+cosx))
= (1 + 2cosx + cos^2x + sin^2x)/(sinx(1+cosx))
= (2+2cosx)/(sinx(1+cosx))
= 2(1+cosx)/(sinx(1+cosx))
= 2/sinx
= 2cscx, but x = 3t
= 2csc(3t)
= RS
2) does not work the way you typed it. 
Math Help 
suzi,
(sin^2 è+ cos^2 è)^3 =1

Math Help 
Reiny,
(sin^2 è+ cos^2 è)^3 =1
That is much too easy!!!!
what is the value of sin^2 è+ cos^2 è ?