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

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Answer

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

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 $\cos(2A)$ is $2\cos^2(A) - 1$.

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

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

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

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