What is the value of cos^2(157.5)-sin^2(157.5) ?

The value of cos^2(157.5)-sin^2(157.5) is (sqrt(2))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^2(157.5)-sin^2(157.5)

cos^{2} (157. 5^{\circ}) - sin^{2} (157. 5^{\circ})

\frac{2}{2}

Solution steps

cos^{2} (157. 5^{\circ}) - sin^{2} (157. 5^{\circ})

Rewrite using trig identities:

cos^{2} (157. 5^{\circ}) = 1 - sin^{2} (157. 5^{\circ})

= 1 - sin^{2} (157. 5^{\circ}) - sin^{2} (157. 5^{\circ})

Simplify

= 1 - 2 sin^{2} (157. 5^{\circ})

Rewrite using trig identities:

sin (157. 5^{\circ}) = sin (22. 5^{\circ})

= 1 - 2 sin^{2} (22. 5^{\circ})

Rewrite using trig identities:

cos (4 5^{\circ})

= cos (4 5^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

= \frac{2}{2}

arccos (sin (- \frac{5 π}{6}))

arcsin (sin (- \frac{3 π}{4}))

30 \cdot cos (4 5^{\circ})

sin (\frac{9}{4} π)

cos (arctan (- \frac{3}{4}))

What is the value of cos^2(157.5)-sin^2(157.5) ?
The value of cos^2(157.5)-sin^2(157.5) is (sqrt(2))/2