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How will you prove it?
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- Scarlet ManukaLv 77 years agoFavorite Answer
cos θ + sec θ = 5/2
=> cos θ + 1/cos θ = 5/2
(You should be able to see that the answer will be cos θ = 1/2, but let's prove it:)
=> 2 cos² θ - 5 cos θ + 2 = 0
=> (2 cos θ - 1) (cos θ - 2) = 0
=> cos θ = 2 or 1/2, but we know it can't be 2.
So cos θ = 1/2 and sec θ = 1/cos θ = 2.
Hence cos^n θ + sec^n θ = (1/2)^n + 2^n = 2^n + 2^(-n).
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