Posted by **suzi** on Saturday, February 26, 2011 at 2:57pm.

1) 1+cos(3t)/ sin(3t) + sin(3t)/( 1+ cos(3t))= 2csc(3t)

2) sec^2 2u-1/ sec^2 2u= sin^2 2u

3) cosB/1- sinB= secB+ tanB

- Math Help -
**Reiny**, Saturday, February 26, 2011 at 3:07pm
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/(1-sinB) = secB + tanB

then:

RS = 1/cosB + sinB/cosB

= = (1-sinB)/cosB * (1+sinB)/(1+sinB)

= (1 - sin^2 B)/(cosB(1+sinB)

= cos^2B/(cosB(1+sinB))

= cosB/(1+sinB)

= LS

- Math Help -
**suzi**, Saturday, February 26, 2011 at 3:16pm
1)1+cos(3t)/ sin(3t) + sin(3t)/( 1+ cos(3t))= 2csc(3t)

2)sec^2 (2u-1)/ sec^2 (2u)= sin^2 (2u)

- Math Help -
**Reiny**, Saturday, February 26, 2011 at 3:32pm
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**, Saturday, February 26, 2011 at 3:43pm
(sin^2 è+ cos^2 è)^3 =1

- Math Help -
**Reiny**, Saturday, February 26, 2011 at 3:55pm
(sin^2 è+ cos^2 è)^3 =1

That is much too easy!!!!

what is the value of sin^2 è+ cos^2 è ?

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