Question

Find the value of theta if 7sin^2 theta + 3 cos^2 theta =4

Answer 1

Given: 7 sin²∅ + 3 cos²∅ = 4

Since we know very well that cos²∅ = 1 - sin²∅.

Hence by replacing value we get,

→ 7 sin²∅ + 3(1 - sin²∅) = 4

→ 7 sin²∅ + 3 - 3 sin²∅ = 4

→ 4 sin²∅ = 4 - 3

→ sin²∅ = ¼

→ (sin∅)² = ¼

→ sin∅ = ½

Since sin 30° = ½, therefore:

→ sin∅ = sin30°

→ ∅ = 30°

Hence value of thera (∅) is 30°.

Answer 2

Step-by-step explanation:

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 .