What is the value of tan^2(arctan(2))+cot^2(arccot(3)) ?

The value of tan^2(arctan(2))+cot^2(arccot(3)) is 13

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tan^2(arctan(2))+cot^2(arccot(3))

tan^{2} (arctan (2)) + cot^{2} (arccot (3))

13

Solution steps

tan^{2} (arctan (2)) + cot^{2} (arccot (3))

Rewrite using trig identities:

cot (arccot (3)) = 3

Use the following identity:

cot (arccot (x)) = x

= 3

= tan^{2} (arctan (2)) + 3^{2}

Simplify

= tan^{2} (arctan (2)) + 9

Rewrite using trig identities:

tan (arctan (2)) = 2

Use the following identity:

tan (arctan (x)) = x

= 2

= 2^{2} + 9

Simplify

= 13

20 cos (5 3^{\circ})

cos (\frac{53 \cdot π}{180}) \cdot 4.5

\frac{sin ( \frac{23. 2 ^{\circ} + 6 0 ^{\circ}}{2} )}{sin ( \frac{6 0 ^{\circ}}{2} )}

4 sin (33 0^{\circ})

3 cos (27 0^{\circ})

What is the value of tan^2(arctan(2))+cot^2(arccot(3)) ?
The value of tan^2(arctan(2))+cot^2(arccot(3)) is 13