...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.

(Looking for rad. answers in the range)

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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 ...