Question

Use the equations 8x² −4xy+5y² =36 to find tan(2θ).

a) −4/3
b) −3/4
c) 4/3
d) 3/4

Answer 1

To find tan(2θ) from the equation 8x² −4xy+5y² =36, we can manipulate the equation to express it in terms of tan(θ) and then solve for tan(2θ).

Step-by-step explanation:

To find tan(2θ) from the equation 8x² −4xy+5y² =36, we can manipulate the equation to express it in terms of tan(θ) and then solve for tan(2θ). Here are the steps:

1. Divide both sides of the equation by x² to obtain: 8 - 4y/x + 5(y/x)² = 36/x²
2. Let u = y/x, this transforms the equation to: 8 - 4u + 5u² = 36/x²
3. Now, express tan(θ) in terms of u: tan(θ) = u = y/x
4. Now, find tan(2θ) by substituting 2θ for θ in the expression for tan(θ): tan(2θ) = 2u/(1 - u²)

By substituting u = y/x into the expression for tan(2θ), we can find the value of tan(2θ).