Question
If θ is a positive acute angle and cos²
θ + cos⁴θ = 1, then the value of tan²θ + tan⁴θ is?Solution
cos² θ + cos ⁴ θ = 1 cos ⁴ θ = 1 - cos² θ cos ⁴ θ = sin² θ cos² θ = sin² θ/ cos² θ tan² θ = cos² θ tan² θ = cos ⁴ θ tan² θ + tan ⁴ θ = cos² θ + cos ⁴ θ = 1
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