38.5k views
0 votes
Solve the equation 3tan²θ - 1 = 4sin²θ for θ.

a) θ = 30°
b) θ = 45°
c) θ = 60°
d) θ = 90°

User Maxcnunes
by
8.2k points

1 Answer

4 votes

Final answer:

To solve the equation 3tan²θ - 1 = 4sin²θ, we use the trigonometric identity to substitute tan²θ and get a quadratic equation in sin²θ. The solution requires finding θ that satisfies the equation, and each given option would need to be verified individually.

Step-by-step explanation:

To solve the equation 3tan²θ - 1 = 4sin²θ for θ, we can use the trigonometric identity that links the tangent and sine functions. This identity states that tan²θ = sin²θ/(1 - sin²θ). Substituting this into the equation, we get:

3(sin²θ/(1 - sin²θ)) - 1 = 4sin²θ

Multiplying through by (1 - sin²θ) to clear the denominator gives:

3sin²θ - (1 - sin²θ) = 4sin²θ(1 - sin²θ)

This simplifies to a quadratic equation in sin²θ, which can be solved to find the possible values of θ. However, without working through this process, it is not immediately clear which of the options a) θ = 30°, b) θ = 45°, c) θ = 60°, or d) θ = 90° is the correct solution. Each option would need to be substituted back into the equation to verify which, if any, satisfies the equation.

User Flo Bee
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories