use a double - angle identity to find the exact value of the expression. $\\cos ^{2}90^{\\circ }-\\sin…

use a double - angle identity to find the exact value of the expression. $\\cos ^{2}90^{\\circ }-\\sin ^{2}90^{\\circ }$ $\\cos ^{2}90^{\\circ }-\\sin ^{2}90^{\\circ }=$ (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. $\\cos ^{2}90^{\\circ }-\\sin ^{2}90^{\\circ }$ $\\cos ^{2}90^{\\circ }-\\sin ^{2}90^{\\circ }=$ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall the double - angle identity

The double - angle identity for cosine is (\cos2\alpha=\cos^{2}\alpha - \sin^{2}\alpha).

Step2: Substitute (\alpha = 90^{\circ})

When (\alpha = 90^{\circ}), we have (\cos^{2}90^{\circ}-\sin^{2}90^{\circ}=\cos(2\times90^{\circ})).

Step3: Calculate (\cos(2\times90^{\circ}))

Since (2\times90^{\circ}=180^{\circ}), and (\cos180^{\circ}=- 1).

Answer:

(-1)