prove 3sec^2(x)-4=0

Solution

prove

3 sec^{2} (x) - 4 = 0

False

Solution steps

3 sec^{2} (x) - 4 = 0

Show that the two sides are not equal

For

3 sec^{2} (x) - 4 = 0

plug in

x = 0

3 sec^{2} (0) - 4 = - 1

3 sec^{2} (0) - 4

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

= 3 \cdot 1^{2} - 4

Simplify

= - 1

The two sides are not equal

\Rightarrow False

sin (3 θ) = 3 sin (θ) - 4 sin (3 θ)

(sec^{2} (x) cot (x)) + cot (x) = tan (x)

cos (- \frac{1}{2}) = cos (\frac{2}{2})

(\frac{1}{2} sin^{2} (θ)) = (\frac{1}{2} cos (2 θ))

(sin (3 x) + cos (3 x))^{2} = 1 + sin (6 x)