Solve 2cotx + sec^2x = 0?

this is as far as i have gotten:

2cotx + sec^2x = 0

2/tanx + tan^2x + 1 = 0

and thats it. can someone please help me with the solution and explain each step?

1 Answer

  • Elementary, I assure you…

    2cotx + sec^2x = 0

    2/tanx + tan^2x + 1 = 0

    Now multiply through by tanx:

    tan^3x + tanx + 2 = 0

    By inspection, tanx = -1 is a root, in fact the only one, as synthetic division would confirm.

    But if tanx = -1, then x = (4n+3)π/4, so for example 3π/4, 7π/4 etc.

    Caio!

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