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Gnesinka [82]
2 years ago
11

Cos(2x) + sin^2(x) = 0

Mathematics
1 answer:
zloy xaker [14]2 years ago
7 0

cos(2<em>θ</em>) + sin²(<em>θ</em>) = 0

Half-angle identity:

cos(2<em>θ</em>) + (1 - cos(2<em>θ</em>))/2 = 0

Simplify:

2 cos(2<em>θ</em>) + 1 - cos(2<em>θ</em>) = 0

cos(2<em>θ</em>) = -1

Solve for <em>θ</em> :

2<em>θ</em> = arccos(-1) + 2<em>nπ</em>

2<em>θ</em> = <em>π</em> + 2<em>nπ</em>

<em>θ</em> = <em>π</em>/2 + <em>nπ</em>

where <em>n</em> is any integer.

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