Find the exact value of the expression.884:890
-$\cos \left[ 2 \sin ^ { - 1 } \left( - \frac { 5 } { 13 } \right) \right]$
A) $\frac { 119 } { 169 }$

B) $\frac { 10 } { 13 }$

C) $- \frac { 12 } { 13 }$

D) $\frac { 2 \sqrt { 5 } + 10 } { 13 }$

Question

Find the exact value of the expression.884:890
-$\cos \left[ 2 \sin ^ { - 1 } \left( - \frac { 5 } { 13 } \right) \right]$
A) $\frac { 119 } { 169 }$

B) $\frac { 10 } { 13 }$

C) $- \frac { 12 } { 13 }$

D) $\frac { 2 \sqrt { 5 } + 10 } { 13 }$

Quizplus · Accepted Answer

To find the exact value of the expression $884:890 \cos \left[ 2 \sin ^ { - 1 } \left( - \frac { 5 } { 13 } \right) \right]$, we use the double angle formula for cosine, which is $\cos(2\theta) = 1 - 2\sin^2(\theta)$. Given $\sin^{-1}\left(-\frac{5}{13}\right)$, we know $\sin(\theta) = -\frac{5}{13}$. Plugging this into the double angle formula, we get $\cos(2\theta) = 1 - 2\left(-\frac{5}{13}\right)^2 = 1 - 2\left(\frac{25}{169}\right) = 1 - \frac{50}{169} = \frac{119}{169}$.

Find the Exact Value of the Expression cos⁡[2sin⁡−1(−513)]\cos \left[ 2 \sin ^ { - 1 } \left( - \frac { 5 } { 13 } \right) \right]cos[2sin−1(−135​)]

Find the Exact Value of the Expression $\cos \left[ 2 \sin ^ { - 1 } \left( - \frac { 5 } { 13 } \right) \right]$