If 7 sin^{2} θ + 3 cos^{2} θ = 4, (0° < θ < 90°), then the value of tanθ is

Question 142

If $$7 sin^{2} θ + 3 cos^{2} θ = 4$$, (0° < θ < 90°), then the value of tanθ is

Solution

$$7 sin^{2} θ + 3 cos^{2} θ = 4$$

$$\rightarrow7 sin^{2} θ + 3 - 3sin^{2} θ = 4$$

$$\rightarrow4 sin^{2} θ = 1$$

$$\rightarrow$$sin θ = $$\pm\frac{1}{2}$$

but (0° < θ < 90°) so θ = 30

then tan θ = tan30 = $$\frac{1}{\sqrt{3}}$$

so the answer is option A.

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