Question

What is the value of 2cos2(105⁰) − 1? Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction Negative one-half One-half StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Answer 1

Answer: - sqrt3/2

Explanation:

Answer 2

`-(√(3))/(2)`

Explanation:

To find the exact value of 2cos²(105°) - 1, we can use the Cosine Double Angle identity.

`\boxed{\begin{array}{c}\underline{\textsf{Cosine Double Angle Identity}}\\\\\cos (2 \theta)=2 \cos^2 \theta - 1\end{array}}`

In our case, θ = 105°. Therefore:

`2\cos^2\left(105^(\circ)\right)-1=\cos(2 \cdot 105^(\circ))`

`2\cos^2\left(105^(\circ)\right)-1=\cos(210^(\circ))`

According to the unit circle:

`\cos(210^(\circ))=-(√(3))/(2)`

Therefore:

`2\cos^2\left(105^(\circ)\right)-1=-(√(3))/(2)`