Is cos(x)-cos(x)=2cos(x) ?

The answer to whether cos(x)-cos(x)=2cos(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(x)-cos(x)=2cos(x)

prove

cos (x) - cos (x) = 2 cos (x)

False

Solution steps

cos (x) - cos (x) = 2 cos (x)

Show that the two sides are not equal

For

cos (x) - cos (x) = 2 cos (x)

plug in

x = 0

cos (0) - cos (0) = 0

cos (0) - 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 - 1

Simplify

= 0

2 cos (0) = 2

2 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

= 2 \cdot 1

Simplify

= 2

The two sides are not equal

\Rightarrow False

\frac{cos ^{2} ( 2 θ )}{2} = \frac{1 + cos ( 4 θ )}{8}

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

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

(sin (2 θ)) (tan (θ)) + cos (2 θ) = 1

cot (x) - cot (x) cos^{2} (x) = sin (x) cos (x)