Is (cos(θ)+cos(3θ))/(2cos(θ))=cos(2θ) ?

The answer to whether (cos(θ)+cos(3θ))/(2cos(θ))=cos(2θ) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove (cos(θ)+cos(3θ))/(2cos(θ))=cos(2θ)

prove

\frac{cos ( θ ) + cos ( 3 θ )}{2 cos ( θ )} = cos (2 θ)

True

Solution steps

\frac{cos ( θ ) + cos ( 3 θ )}{2 cos ( θ )} = cos (2 θ)

Manipulating left side

\frac{cos ( θ ) + cos ( 3 θ )}{2 cos ( θ )}

Rewrite using trig identities

= cos (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

3 tan (x) = 4 sin (x)

sin (x) + cos (x) = 2 sin (x + \frac{π}{4})

(sin (t)) cot (t) = cos (t)

Is (cos(θ)+cos(3θ))/(2cos(θ))=cos(2θ) ?
The answer to whether (cos(θ)+cos(3θ))/(2cos(θ))=cos(2θ) is True