Question

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Answer 1

Answer:

Step-by-step explanation:

so, given

7 sin^2θ + 3 cos^2θ = 4

7 sin^2θ + 3(1 - sin^2θ) = 4

(as, sin^2θ + cos^2θ = 1)

so,

7 sin^2θ + 3 - 3 sin^2θ = 4

4 sin^2θ = 4-3

sin^2θ = 1/4

sinθ = √1/4

sinθ = 1/2

so

cos^2θ = 1 - sin^2θ

cos^2θ = 1 - 1/4                         (by substituting the value of sin^2θ)

cos^2θ =3/4

cosθ = √3/4 = √(3)/2

so,

tanθ = sinθ/cosθ

tanθ = (1/2)/(√(3)/2)

tanθ = (1/2) * (2/√(3))

tanθ = 1/√3

so, hence proved.