Consider \( \cos ^{n} x-\sin ^{n} x=1 \), where \( n \) is a natura...

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Consider \( \cos ^{n} x-\sin ^{n} x=1 \), where \( n \) is a natural number and \( -\pix \leq \pi \)
When \( n=1 \), the sum of the values of \( x \) satisfying the equation is
(a) \( -\pi / 2 \)
(b) 0
(c) \( \pi / 4 \)
(d) \( \pi / 2 \)
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