Question

7sin^2 theta + cos^2 theta = 44 prove that tan theta = 1/√3​

Answer 1

Answer:

tan30° = 1/√3

Step-by-step explanation:

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°

∴ ∅ = 30

tan 30° = 1/√3 .

Hence, it is proved .

Answer 2

Step-by-step explanation:

To prove:

$7{sin}^{2} x + {cos}^{2} x = 44$

Given: tanx = 1/√3

=> x = 30°

Substitute x = 30° in given equation

$7{sin}^{2} (30) - {cos}^{2} (30) \\ = 7( \frac{1}{4} ) - ( \frac{3}{4} ) = \frac{7}{4} - \frac{3}{4} \\ \frac{7 - 3}{4} = \frac{4}{4} = 1$

I think the question is wrong as answer will come 4/4=1 and not 44 affording to the given equation and conditions