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sec^4x=11tan^2x+5 than what is the value of tanx

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sec^4x=11tan^2x+5
(1+tan^2x)^2 = 11tan^2x+5
tan^4x + 2tan^2x + 1 - 11tan^2x - 5 = 0
tan^4x - 9tan^2x - 4 = 0

That's just a quadratic in tan^2x, so solve it, then just take the square root.

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