Find $\cos (2 A)$ , if $\cos (A) = - \frac{21}{29}$ , and $A$ is in quadrant 3 .
Write in fraction form

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\frac{41}{841}$

Steps

Step 1 ：We are given that $\cos (A) = - \frac{21}{29}$ and that $A$ is in the third quadrant.

Step 2 ：We know that the formula for $\cos (2 A)$ is $2 \cos^{2} (A) - 1$ .

Step 3 ：Substitute $\cos (A)$ into the formula to find $\cos (2 A)$ .

Step 4 ： $\cos (2 A) = 2 (- \frac{21}{29})^{2} - 1$

Step 5 ：Simplify to get $\cos (2 A) = \frac{41}{841}$

Step 6 ：Final Answer: $\frac{41}{841}$