use a double - angle identity to find the exact value of the expression.\n\n\\( \\cos ^ { 2 } 45 ^ { \\circ…

use a double - angle identity to find the exact value of the expression.\n\n\\( \\cos ^ { 2 } 45 ^ { \\circ } - \\sin ^ { 2 } 45 ^ { \\circ } \\)\n\n\\( \\cos ^ { 2 } 45 ^ { \\circ } - \\sin ^ { 2 } 45 ^ { \\circ } = \\square \\)\n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

use a double - angle identity to find the exact value of the expression.\n\n\\( \\cos ^ { 2 } 45 ^ { \\circ } - \\sin ^ { 2 } 45 ^ { \\circ } \\)\n\n\\( \\cos ^ { 2 } 45 ^ { \\circ } - \\sin ^ { 2 } 45 ^ { \\circ } = \\square \\)\n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Apply double - angle identity

The double - angle identity for cosine is (\cos2\alpha=\cos^{2}\alpha - \sin^{2}\alpha). Let (\alpha = 45^{\circ}), then (\cos^{2}45^{\circ}-\sin^{2}45^{\circ}=\cos(2\times45^{\circ})).

Step2: Simplify the angle

(2\times45^{\circ}=90^{\circ}), so (\cos(2\times45^{\circ})=\cos90^{\circ}).

Step3: Evaluate (\cos90^{\circ})

We know that (\cos90^{\circ}=0).

Answer:

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