Is (3sin^2(2x))/2 =(3cos(4x))/4 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove (3sin^2(2x))/2 =(3cos(4x))/4

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

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

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

Refine to a decimal form

= 0

\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

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