What is the value of tan^2(60)-sec^2(60)+cot(45) ?

The value of tan^2(60)-sec^2(60)+cot(45) is 0

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tan^2(60)-sec^2(60)+cot(45)

tan^{2} (6 0^{\circ}) - sec^{2} (6 0^{\circ}) + cot (4 5^{\circ})

0

Solution steps

tan^{2} (6 0^{\circ}) - sec^{2} (6 0^{\circ}) + cot (4 5^{\circ})

Use the following trivial identity:

tan (6 0^{\circ}) = 3

tan (6 0^{\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}

= 3

Use the following trivial identity:

sec (6 0^{\circ}) = 2

sec (6 0^{\circ})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

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

= (3)^{2} - 2^{2} + 1

Simplify

(3)^{2} - 2^{2} + 1 : 0

(3)^{2} - 2^{2} + 1

(3)^{2} = 3

(3)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

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

\frac{1}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

2

= 1

= 3

= 3 - 2^{2} + 1

Add the numbers:

3 + 1 = 4

= 4 - 2^{2}

2^{2} = 4

= 4 - 4

Subtract the numbers:

4 - 4 = 0

= 0

= 0

cos (arctan (2))

sin (\frac{2 π}{3}) - cos (\frac{π}{12}) + tan (\frac{5 π}{4})

sin (5 0^{\circ}) sin (1 0^{\circ}) - 2 cos (4 0^{\circ}) - 2 cos (2 0^{\circ})

3 sin (\frac{π}{3}) - \frac{1}{2} cos^{2} (\frac{π}{3}) - \frac{7}{8}

cos (\frac{3 π}{4}) + i \cdot sin (\frac{3 π}{4})

What is the value of tan^2(60)-sec^2(60)+cot(45) ?
The value of tan^2(60)-sec^2(60)+cot(45) is 0