To solve this equation, we can first rewrite it in terms of sin(2x) using the identity sin(2x) = 2sin(x)cos(x).
So, 2sin(x)cos(x) + 5cos^2(x) = 4 can be rewritten as 2sin(x)cos(x) + 5cos^2(x) = 4.
Now, we substitute sin(2x) = 2sin(x)cos(x) into the equation, we get:
sin(2x) + 5cos^2(x) = 4.
Next, we can use the Pythagorean identity cos^2(x) = 1 - sin^2(x) to rewrite the equation as:
sin(2x) + 5(1 - sin^2(x)) = 4.
Solving for sin(2x), we get:
sin(2x) = 4 - 5 + 5sin^2(x).sin(2x) = 5sin^2(x) - 1.
This is a quadratic equation in terms of sin(x), which can be solved by setting it equal to zero and factoring or using the quadratic formula.
To solve this equation, we can first rewrite it in terms of sin(2x) using the identity sin(2x) = 2sin(x)cos(x).
So, 2sin(x)cos(x) + 5cos^2(x) = 4 can be rewritten as 2sin(x)cos(x) + 5cos^2(x) = 4.
Now, we substitute sin(2x) = 2sin(x)cos(x) into the equation, we get:
sin(2x) + 5cos^2(x) = 4.
Next, we can use the Pythagorean identity cos^2(x) = 1 - sin^2(x) to rewrite the equation as:
sin(2x) + 5(1 - sin^2(x)) = 4.
Solving for sin(2x), we get:
sin(2x) = 4 - 5 + 5sin^2(x).
sin(2x) = 5sin^2(x) - 1.
This is a quadratic equation in terms of sin(x), which can be solved by setting it equal to zero and factoring or using the quadratic formula.