Is (3)((cos(2z))^2)/2 =(3cos(4z))/4 ?

The answer to whether (3)((cos(2z))^2)/2 =(3cos(4z))/4 is False

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prove (3)((cos(2z))^2)/2 =(3cos(4z))/4

prove

(3) \frac{( cos ( 2 z ) ) ^{2}}{2} = \frac{3 cos ( 4 z )}{4}

False

Solution steps

3 \cdot \frac{( cos ( 2 z ) ) ^{2}}{2} = \frac{3 cos ( 4 z )}{4}

Show that the two sides are not equal

For

3 \frac{cos ^{2} ( 2 z )}{2} = \frac{3 cos ( 4 z )}{4}

plug in

z = 0

3 \cdot \frac{cos ^{2} ( 2 \cdot 0 )}{2} = \frac{3}{2} (Decimal : 1.5)

3 \cdot \frac{cos ^{2} ( 2 \cdot 0 )}{2}

Simplify:

2 \cdot 0 = 0

2 \cdot 0

Apply rule

0 \cdot a = 0

= 0

3 \cdot \frac{cos ^{2} ( 0 )}{2} = \frac{3 cos ^{2} ( 0 )}{2}

3 \cdot \frac{cos ^{2} ( 0 )}{2}

Multiply fractions:

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

= \frac{cos ^{2} ( 0 ) \cdot 3}{2}

= \frac{3 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

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

Simplify

= \frac{3}{2}

\frac{3 cos ( 4 \cdot 0 )}{4} = \frac{3}{4} (Decimal : 0.75)

\frac{3 cos ( 4 \cdot 0 )}{4}

Simplify

= \frac{3 cos ( 0 )}{4}

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{3 \cdot 1}{4}

Simplify

= \frac{3}{4}

The two sides are not equal

\Rightarrow False

- 2 sin^{2} (x) + cos (x) + 1 = 0

\frac{2 cot ( u )}{csc ^{2} ( u ) - 2} = tan (2 u)

csc (2 x) + cot (2 x) = \frac{1 + cos ( 2 x )}{sin ( 2 x )}

1 - 2 sin^{2} (t) = 2 cos^{2} (t) - 1

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

Is (3)((cos(2z))^2)/2 =(3cos(4z))/4 ?
The answer to whether (3)((cos(2z))^2)/2 =(3cos(4z))/4 is False