What is the value of (-2(-2sec^2(0)+3sec^4(0)))/(cos(0)) ?

The value of (-2(-2sec^2(0)+3sec^4(0)))/(cos(0)) is -2

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(-2(-2sec^2(0)+3sec^4(0)))/(cos(0))

\frac{- 2 ( - 2 sec ^{2} ( 0 ) + 3 sec ^{4} ( 0 ) )}{cos ( 0 )}

- 2

Solution steps

\frac{- 2 ( - 2 sec ^{2} ( 0 ) + 3 sec ^{4} ( 0 ) )}{cos ( 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:

cos (0) = 1

cos (0)

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= \frac{- 2 ( - 2 \cdot 1 ^{2} + 3 \cdot 1 ^{4} )}{1}

Simplify

= - 2

sin (9.4)

sin (sin (9 0^{\circ}))

csc (arctan (\frac{4}{3}))

arcsin (- \frac{4}{9})

- tan^{2} (\frac{4 π}{3})

What is the value of (-2(-2sec^2(0)+3sec^4(0)))/(cos(0)) ?
The value of (-2(-2sec^2(0)+3sec^4(0)))/(cos(0)) is -2