Question

Solve the equation: sin(theta) * sec^2(theta) + 3sin(theta) = 7sin(theta).

A) sin(theta) = 7
B) sec^2(theta) = 4
C) sin(theta) = 0
D) theta = 45 degrees

Answer 1

To solve the equation sin(theta) * sec^2(theta) + 3sin(theta) = 7sin(theta), divide both sides by sin(theta), subtract 3 from both sides and take the square root of both sides. The correct answer is B) sec^2(theta) = 4.

Step-by-step explanation:

To solve the equation sin(theta) * sec^2(theta) + 3sin(theta) = 7sin(theta), we can simplify the equation by canceling out sin(theta) on both sides and then solve for theta. Here's the step-by-step process:

1. sin(theta) * sec^2(theta) + 3sin(theta) = 7sin(theta)
2. Divide both sides by sin(theta): sec^2(theta) + 3 = 7
3. Subtract 3 from both sides: sec^2(theta) = 4
4. Take the square root of both sides: sec(theta) = 2 or -2

Therefore, the correct answer is B) sec^2(theta) = 4.