# Thread: Help solve trig func equation and identity

1. ## Help solve trig func equation and identity

Help solve trig func equation and identity

Hello! I have problems with these two questions!

1) Solve for 0<= x <= 2pi
--> cosx (1-2sinx) = 0

------------------------------------------
2) Prove this identity:
--> cosx/(1-sinx) - secx = tanx

(LS = RS)

Would be great to get some steps!

2. Originally Posted by Genuine
Help solve trig func equation and identity

Hello! I have problems with these two questions!

1) Solve for 0<= x <= 2pi
--> cosx (1-2sinx) = 0

set each factor equal to 0 ...

cosx = 0 ... x = ?

sinx = 1/2 ... x = ?

you should know the solutions to these based on your knowledge of the unit circle.

------------------------------------------
2) Prove this identity:
--> cosx/(1-sinx) - secx = tanx

[cosx/(1-sinx)]*[(1+sinx)/(1+sinx)] - secx =

cosx(1+sinx)/(1-sin^2x) - secx =

cosx(1+sinx)/cos^2x - secx =

(1+sinx)/cosx - 1/cosx =

finish ...

...

3. $cosX = 0$

$cos^{-1}\left(0\right) = \frac{\pi}{2}$ and $\frac{3\pi}{2}$
--------------------------------------------------------------

$1 - 2sinX = 0$

$
2sinX = 1
$

$
SinX = \frac{1}{2}
$

$
sin^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{6}$
and $\frac{5\pi}{3}$

4. ## still puzzled with 1)

Thank you very much for the fast response!
I understand 2) [thanks skeeter!]
What exactly do you mean "set each factor equal to 0 ..." ?
Im probly just not familiar with the wording

5. Originally Posted by Genuine
Thank you very much for the fast response!
I understand 2) [thanks skeeter!]
What exactly do you mean "set each factor equal to 0 ..." ?
Im probly just not familiar with the wording
cosx(1-2sinx) = 0

cosx is a factor , (1-2sinx) is a factor

if two or more factors multiply to 0, then each factor has the possibility of equaling 0.

cosx = 0

1-2sinx = 0