Question

If θ be acute angle and 7sin²θ + 3cos²θ = 4, then the value of tanθ is

Answer 1

Hi ,

Here I am using A instead of theta.

7sin²A + 3cos² A = 4

7sin² A + 3 ( 1 - sin² A ) = 4

7sin² A + 3 - 3sin² A = 4

4sin²A = 4 - 3

4sin² A = 1

Sin² A = 1/4

SinA = √1/4

SinA = 1/2

SinA = sin 30°

A = 30°

Tan A = tan 30°

= 1/√3

I hope this helps you.

:)

Answer 2

Answer:

tan Θ = tan30° = 1/√3

Step-by-step explanation:

7sin²Θ + 3cos² Θ = 4

7sin² Θ + 3 ( 1 - sin² Θ ) = 4

7sin² Θ + 3 - 3sin² Θ = 4

4sin²Θ = 4 - 3

4sin² Θ = 1

sin² Θ = 1/4

sinΘ = √1/4

sinΘ = 1/2

sinΘ = sin30°

Θ = 30°

tan Θ = tan30°

= 1/√3