Question

7 sin² theta + 3 cos² theta = 4, find value of theta

Answer 1

7sin2Ɵ + 3cos2Ɵ = 4

=4sin2Ɵ + 3sin2Ɵ + 3cos2Ɵ = 4

=4sin2Ɵ + 3(sin2Ɵ + cos2Ɵ) = 4 (sin2Ɵ + cos2Ɵ =1)

=4sin2Ɵ + 3 = 4

=4sin2Ɵ = 4 – 3 = 1

=sin2Ɵ = 1/4

=sinƟ = √1/4

=sinƟ = 1/2

=sinƟ =sin30 (sin30 = 1/2)

=Ɵ = 30

Answer 2

Answer :-

→ ∅ = 30° .

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° .

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

Hence, it is solved .