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Math Help - trigonometry problem

  1. #1
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    trigonometry problem

    Can someone please explain me how can equation \[sin(\pi -x)+cos^{2}x=1\]<br />
be solved?
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  2. #2
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    \displaystyle \sin{(\pi - x)} = \sin{x}.

    So the equation reduces to

    \displaystyle \sin{x} + \cos^2{x} = 1

    \displaystyle \sin{x} + 1 - \sin^2{x} = 1

    \displaystyle \sin{x} - \sin^2{x} = 0

    \displaystyle \sin{x}(1 - \sin{x}) = 0

    \displaystyle \sin{x} = 0 or \displaystyle 1 - \sin{x} = 0 \implies \sin{x} = 1

    \displaystyle x = \pi n where \displaystyle n is an integer or \displaystyle \frac{\pi}{2} + 2\pi m where \displaystyle m is an integer.
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