What is the value of (tan(45)+cot(45))^2 ?

The value of (tan(45)+cot(45))^2 is 4

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(tan(45)+cot(45))^2

(tan (4 5^{\circ}) + cot (4 5^{\circ}))^{2}

4

Solution steps

(tan (4 5^{\circ}) + cot (4 5^{\circ}))^{2}

Use the following trivial identity:

tan (4 5^{\circ}) = 1

tan (4 5^{\circ})

tan (x)

periodicity table with

18 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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

Use the following trivial identity:

cot (4 5^{\circ}) = 1

cot (4 5^{\circ})

cot (x)

periodicity table with

18 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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

= (1 + 1)^{2}

Simplify

= 4

2 sin (3 (arccos (- \frac{1}{4})))

\frac{tan ( 1 7 ^{\circ} ) + tan ( 1 3 ^{\circ} )}{1 - tan ( 1 7 ^{\circ} ) tan ( 1 3 ^{\circ} )}

arctan (756)

350000 csc (\frac{π}{30} \cdot 5)

cos (arctan (\frac{1}{3}))

What is the value of (tan(45)+cot(45))^2 ?
The value of (tan(45)+cot(45))^2 is 4