What is the value of -8sec^2(0)tan(0)+24sec^4(0)tan(0) ?

The value of -8sec^2(0)tan(0)+24sec^4(0)tan(0) is 0

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-8sec^2(0)tan(0)+24sec^4(0)tan(0)

- 8 sec^{2} (0) tan (0) + 24 sec^{4} (0) tan (0)

0

Solution steps

- 8 sec^{2} (0) tan (0) + 24 sec^{4} (0) tan (0)

Use the following trivial identity:

sec (0) = 1

sec (0)

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 1

Use the following trivial identity:

tan (0) = 0

tan (0)

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

= - 8 \cdot 1^{2} \cdot 0 + 24 \cdot 1^{4} \cdot 0

Simplify

= 0

csc (91 5^{\circ})

arctan (21)

arctan (27)

arctan (1)

arctan (5)

What is the value of -8sec^2(0)tan(0)+24sec^4(0)tan(0) ?
The value of -8sec^2(0)tan(0)+24sec^4(0)tan(0) is 0