Question

If 3cos2θ + 7sin2θ=4 so that cotθ=√3.

Answer 1

Answer:

Step-by-step explanation:

3cos²θ + 7sin²θ=4

To Prove- cotθ = √3

Proof-

We are given that -

3cos²θ + 7sin²θ=4

So,

sin²θ = 1 - cos²θ

Putting the value -

3cos²θ + 7sin²θ=4

3cos²θ + 7(1 - cos²θ) = 4

3cos²θ + 7 - 7cos²θ = 4

-4cos²θ = -3

cos²θ = 3/4

1 - sin²θ = 3/4

-sin²θ = -1/4

sin²θ = 1/4

cot²θ = cos²θ/sin²θ

cot²θ = 1/4/3/4

cot²θ = 3

Taking root on both sides,

cotθ = √3

Hence proved... Pls mark as brainliest

Answer 2

Answer:

Answer:

Step-by-step explanation:

3cos²θ + 7sin²θ=4

To Prove- cotθ = √3

Proof-

We are given that -

3cos²θ + 7sin²θ=4

So,

sin²θ = 1 - cos²θ

Putting the value -

3cos²θ + 7sin²θ=4

3cos²θ + 7(1 - cos²θ) = 4

3cos²θ + 7 - 7cos²θ = 4

-4cos²θ = -3

cos²θ = 3/4

1 - sin²θ = 3/4

-sin²θ = -1/4

sin²θ = 1/4

cot²θ = cos²θ/sin²θ

cot²θ = 1/4/3/4

cot²θ = 3

Taking root on both sides,

cotθ = √3

Hence proved... Pls mark as brainliest