If 7sin²θ + 3cos²θ = 4 and θ is acute, then tanθ equals:

1/√3. Writing cos²θ = 1 − sin²θ gives 4sin²θ + 3 = 4, so sinθ = 1/2, θ = 30° and tanθ = 1/√3.

If 7si $n^{2}$ θ + 3co $s^{2}$ θ = 4 and θ is acute, then tanθ equals:

Competition practiceTrigonometry

Writing co

s^{2}

θ = 1 − si

n^{2}

θ gives 4si

n^{2}

θ + 3 = 4, so sinθ = 1/2, θ = 30° and tanθ = 1/√3.

Answer: C) 1/√3

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