Is cos(4x)=8cos^4(x) ?

The answer to whether cos(4x)=8cos^4(x) is False

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos(4x)=8cos^4(x)

prove

cos (4 x) = 8 cos^{4} (x)

False

Solution steps

cos (4 x) = 8 cos^{4} (x)

Show that the two sides are not equal

For

cos (4 x) = 8 cos^{4} (x)

plug in

x = 0

cos (4 \cdot 0) = 1

cos (4 \cdot 0)

Simplify

= cos (0)

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

= 1

8 cos^{4} (0) = 8

8 cos^{4} (0)

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

= 8 \cdot 1^{4}

Simplify

= 8

The two sides are not equal

\Rightarrow False

((1 + cot (a) - csc (a)) (1 + tan (a) + sec (a))) = 2

\frac{cot ^{2} ( x )}{csc ( x ) - 1} = cot (x) + 1

\frac{sin ^{2} ( x )}{sin ( x )} = \frac{2}{sec ( x )}

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

sin (3 x) = 3 sin (x) - 4 sin (3 x)