prove 4cos^2(x)-2=0

Solution

prove

4 cos^{2} (x) - 2 = 0

False

Solution steps

4 cos^{2} (x) - 2 = 0

Show that the two sides are not equal

For

4 cos^{2} (x) - 2 = 0

plug in

x = 0

4 cos^{2} (0) - 2 = 2

4 cos^{2} (0) - 2

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

= 4 \cdot 1^{2} - 2

Simplify

= 2

The two sides are not equal

\Rightarrow False

cos (2 t) = cos^{2} (t) - sin^{2} (t)

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

sec^{2} (B) - csc^{2} (B) = \frac{tan ( B ) - cot ( B )}{sin ( B ) cos ( B )}

2 + sec (a) cos (a) = 3

5 cos^{2} (θ) + 2 sin^{2} (θ) = 3 cos^{2} (θ) + 2