What is the value of cos(arccot(2)+arccot(3)) ?

The value of cos(arccot(2)+arccot(3)) is (sqrt(2))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

cos(arccot(2)+arccot(3))

cos (arccot (2) + arccot (3))

\frac{2}{2}

Decimal

0.70710 \dots

Solution steps

cos (arccot (2) + arccot (3))

Rewrite using trig identities:

arccot (2) + arccot (3) = arccot (1)

arccot (2) + arccot (3)

Use the Sum to Product identity:

arccot (s) + arccot (t) = arccot (\frac{s t - 1}{t + s})

= arccot (\frac{2 \cdot 3 - 1}{3 + 2})

Simplify

= arccot (1)

= cos (arccot (1))

Rewrite using trig identities:

cos (arccot (1)) = \frac{1 \cdot 1 + 1 ^{2}}{1 + 1 ^{2}}

Use the following identity:

cos (arccot (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{1 \cdot 1 + 1 ^{2}}{1 + 1 ^{2}}

= \frac{1 \cdot 1 + 1 ^{2}}{1 + 1 ^{2}}

Simplify

= \frac{2}{2}

What is the value of cos(arccot(2)+arccot(3)) ?
The value of cos(arccot(2)+arccot(3)) is (sqrt(2))/2