What is the value of cos^2(105)-sin^2(105) ?

The value of cos^2(105)-sin^2(105) is 1-(2+sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos^2(105)-sin^2(105)

cos^{2} (10 5^{\circ}) - sin^{2} (10 5^{\circ})

1 - \frac{2 + 3}{2}

Solution steps

cos^{2} (10 5^{\circ}) - sin^{2} (10 5^{\circ})

Rewrite using trig identities:

cos^{2} (10 5^{\circ}) = 1 - sin^{2} (10 5^{\circ})

= 1 - sin^{2} (10 5^{\circ}) - sin^{2} (10 5^{\circ})

Simplify

= 1 - 2 sin^{2} (10 5^{\circ})

Rewrite using trig identities:

sin (10 5^{\circ}) = \frac{2 ( 3 + 1 )}{4}

= 1 - 2 (\frac{2 ( 3 + 1 )}{4})^{2}

Simplify

1 - 2 (\frac{2 ( 3 + 1 )}{4})^{2} : 1 - \frac{2 + 3}{2}

= 1 - \frac{2 + 3}{2}

arctan (\frac{8}{10})

tan (6 4^{\circ})

2 cos (6 0^{\circ})

cos (arctan (3))

12 sin (6 0^{\circ})

What is the value of cos^2(105)-sin^2(105) ?
The value of cos^2(105)-sin^2(105) is 1-(2+sqrt(3))/2