use a double - angle formula to find the exact value of the given expression.\n1 - 2\\sin^{2}15^{circ}\n1…
use a double - angle formula to find the exact value of the given expression.\n1 - 2\\sin^{2}15^{circ}\n1 - 2\\sin^{2}15^{circ}=\\square\n(simplify your answer, including any radicals. use integers or fractions for any number
Answer
Explanation:
Step1: Recall the double - angle formula
The double - angle formula for cosine is $\cos2\alpha=1 - 2\sin^{2}\alpha$.
Step2: Substitute $\alpha = 15^{\circ}$
When $\alpha = 15^{\circ}$, the given expression $1 - 2\sin^{2}15^{\circ}$ becomes $\cos(2\times15^{\circ})$.
Step3: Calculate the value
Since $2\times15^{\circ}=30^{\circ}$, and $\cos30^{\circ}=\frac{\sqrt{3}}{2}$.
Answer:
$\frac{\sqrt{3}}{2}$