Question

I’m doing old assignments and I don’t remember what I’m supposed to do

Answer 1

Explanation

We are given the following:

`\cos\theta=(12)/(37)`

We are required to determine the value of cos 2Θ.

We know that the double angle identity states:

`\begin{gathered} \cos2\theta=2\cos^2\theta-1 \\ where \\ \cos^2\theta=(\cos\theta)^2 \end{gathered}`

Therefore, we can evaluate cos 2Θ as:

`\begin{gathered} \cos\text{ }2\theta=2\cos^2\theta-1 \\ \cos\text{ }2\theta=2(\cos\theta)^2-1 \\ \cos2\theta=2((12)/(37))^2-1 \\ \cos2\theta=2((144)/(1369))-1 \\ \cos2\theta=(288)/(1369)-1 \\ \cos2\theta=-(1081)/(1369) \end{gathered}`

Hence, the answer is:

`\cos2\theta=-(1081)/(1369)`