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

(Looking for rad. answers in the range)

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2) Prove this identity:

--> cosx/(1-sinx) - secx = tanx

(LS = RS)

Would be great to get some steps!