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

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

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

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

\frac{2}{2}

Decimal Notation

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}

arctan (\frac{2 3}{3})

sin (- 3 0^{\circ}) + sin (15 0^{\circ})

2 arcsin (\frac{3}{2})

arctan (\frac{40}{9})

(2 cos (\frac{π}{12}) + 2 i sin (\frac{π}{12}))^{4}

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