Question

If 7 sin^2 theta + 3 cos^2 theta = 4, prove that, tan theta= 1/root3

Answer 1

7sin²θ + 3cos²θ = 4
7sin²θ + ౩(1-sin²θ) = 4
7sin²θ+3-3sin²θ = 4
4sin²θ+3 = 4
4sin²θ=1
sin²θ = 1/4
sinθ = +1/2
sinθ = +  π/6
Therefore tan θ = + π/6
then we get tan θ = + 1/√3
 
As the required answer is tan θ = + 1/√3 (here we considered  θ =+ π/6)

Answer 2

Answer :-

→ tan30° = 1/3 .

Step-by-step explanation :-

We have,

→ 7 sin² ∅ + 3 cos² ∅ = 4 .

⇒ 4 sin²∅ + 3 sin²∅ + 3 cos²∅ = 4 .

⇒ 4 sin²∅ + 3( sin²∅ + cos²∅ ) = 4 .

⇒ 4 sin²∅ + 3( 1 ) = 4 . [ ∵ sin²∅ + cos²∅ = 1 ] .

⇒ 4 sin²∅ + 3 = 4 .

⇒ 4 sin²∅ = 4 - 3 .

⇒ 4 sin²∅ = 1 .

⇒ sin²∅ = 1/4 .

⇒ sin ∅ = √(1/4) .

∴ sin ∅ = 1/2 .

But, sin 30° = 1/2 .

Then, sin ∅ = sin 30° .

$\huge \pink{ \boxed{ \it \therefore \theta = 30 \degree.}}$

Then, tan 30° = 1/√3 .

Hence, it is proved .