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 numbers in the expression.)

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 numbers in the expression.)

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})). So, (1 - 2\sin^{2}15^{\circ}=\cos30^{\circ}).

Step3: Find the value of (\cos30^{\circ})

We know that (\cos30^{\circ}=\frac{\sqrt{3}}{2}).

Answer:

(\frac{\sqrt{3}}{2})