1.

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). \(\sqrt 3\)

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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