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What is the solution to sec plus tan equals cos over 1 plus sin?
Kaseddon
sec + tan = cos /(1 + sin)
sec and tan are defined so cos is non-zero.
1/cos + sin/cos = cos/(1 + sin)
(1 + sin)/cos = cos/(1 + sin)
cross-multiplying, (1 + sin)2 = cos2
(1 + sin)2 = 1 - sin2
1 + 2sin + sin2 = 1 - sin2
2sin2 + 2sin = 0
sin2 + sin = 0
sin(sin + 1) = 0
so sin = 0 or sin = -1
But sin = -1 implies that cos = 0 and cos is non-zero.
Therefore sin = 0 or the solutions are k*pi radians where k is an integer.
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∙ 10y ago
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