Question

Let θ be an acute angle. If cos2θ + cos2θ = 1, then cosθ = _____.

Answer 1

Answer:
None of the given choices
cos θ = sqrt(3) / 2

Explanation:
cos 2θ + cos 2θ = 1
2 cos 2θ = 1
cos 2θ = 0.5

Now, to get the value of θ, we would need to use the rules of double the angle attached in the figure.

I will use:
cos 2θ = 2 cos²θ - 1

Substitute with cos 2θ = 0.5 and solve for cos θ as follows:
cos 2θ = 2 cos²θ - 1
0.5 = 2 cos²θ - 1
2cos ²θ = 0.5 + 1 = 3/2
cos²θ = 3/4 = 0.75
cos θ = ±√0.75

Since we are given that θ is acute, therefore, θ belongs to the first quadrant which means that cos θ is positive

Based on the above:
cos θ = √0.75 = √3 / 2

Hope this helps :)