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If 7 sin2θ + 3 cos2θ = 4, and θ is a positive acute angle, then tan θ is equal to 1). 1/32). 1/73). \(\frac{1}{{\sqrt 3 }}\)4). \(\sqrt 3\) |
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Answer» We know, SIN2θ + cos2θ = 1 Given, 7 sin2θ + 3 cos2θ = 4 ⇒ 4sin2θ + 3(sin2θ + cos2θ) = 4 ⇒ 4sin2θ + 3 = 4 ⇒ sin2θ = ¼ ⇒ sinθ = ½ or -1/2 Given, θ is a POSITIVE ACUTE angle ∴ sinθ = 1/2 As, sin 30° = ½ ∴ sinθ = sin 30° ⇒ θ = 30° We have to find the value of tanθ = tan30° = 1/√3 |
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