Is cos(4x)=1-8cos^2(x)+8cos^4(x) ?

The answer to whether cos(4x)=1-8cos^2(x)+8cos^4(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos(4x)=1-8cos^2(x)+8cos^4(x)

prove

cos (4 x) = 1 - 8 cos^{2} (x) + 8 cos^{4} (x)

True

Solution steps

cos (4 x) = 1 - 8 cos^{2} (x) + 8 cos^{4} (x)

Manipulating left side

cos (4 x)

Rewrite using trig identities

= 8 cos^{4} (x) - 8 cos^{2} (x) + 1

= 1 - 8 cos^{2} (x) + 8 cos^{4} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

(1 - sin (x)) (1 + sin (x)) = \frac{1}{sec ^{2} ( x )}

\frac{csc ( θ ) + sec ( θ )}{tan ( + 1 )} = csc (θ)

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

cot (x) - 1 = cos (x) (csc (x) - sec (x))

Is cos(4x)=1-8cos^2(x)+8cos^4(x) ?
The answer to whether cos(4x)=1-8cos^2(x)+8cos^4(x) is True