What is the value of cos(65)cos(5)+sin(65)sin(5) ?

The value of cos(65)cos(5)+sin(65)sin(5) is 1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(65)cos(5)+sin(65)sin(5)

cos (6 5^{\circ}) cos (5^{\circ}) + sin (6 5^{\circ}) sin (5^{\circ})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

cos (6 5^{\circ}) cos (5^{\circ}) + sin (6 5^{\circ}) sin (5^{\circ})

Rewrite using trig identities:

cos (6 0^{\circ})

cos (6 5^{\circ}) cos (5^{\circ}) + sin (6 5^{\circ}) sin (5^{\circ})

Use the Angle Difference identity:

cos (s) cos (t) + sin (s) sin (t) = cos (s - t)

= cos (6 5^{\circ} - 5^{\circ})

Simplify

= cos (6 0^{\circ})

= cos (6 0^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= \frac{1}{2}

cos^{3} (18 0^{\circ})

\frac{8}{sin ( 3 5 ^{\circ} )}

sec (7 1^{\circ}) (3 0^{\circ})

9.8 cos (7 5^{\circ})

1 + cos (3 0^{\circ})

What is the value of cos(65)cos(5)+sin(65)sin(5) ?
The value of cos(65)cos(5)+sin(65)sin(5) is 1/2