Question

Show that the equation 4 cosine theta - 1 = 2 sine theta tangent theta can be written in the form:

A. 6cos⁡²θ−cos⁡θ−2=0
B. 5cos⁡²θ−cos⁡θ−1=0
C. 4cos⁡²θ−cos⁡θ−1=0
D. 3cos⁡²θ−cos⁡θ−3=0

Answer 1

The equation 4cos(theta) - 1 = 2sin(theta)tan(theta) can be simplified and rewritten as 6cos^2(theta) - cos(theta) - 2 = 0.

Step-by-step explanation:

Given the equation 4cos(theta) - 1 = 2sin(theta)tan(theta), we can simplify it using trigonometric identities. First, we know that tan(theta) = sin(theta) / cos(theta). So let's substitute that into the equation:

4cos(theta) - 1 = 2sin(theta) * (sin(theta) / cos(theta))

Simplifying further, we get:

4cos(theta) - 1 = 2sin^2(theta) / cos(theta)

Multiplying both sides by cos(theta) to clear the denominator:

4cos^2(theta) - cos(theta) = 2sin^2(theta)

Rearranging the terms:

6cos^2(theta) - cos(theta) - 2 = 0

Therefore, the equation can be written in the form 6cos^2(theta) - cos(theta) - 2 = 0.