Is cos(θ-60)+cos(θ+60)=cos(θ) ?

The answer to whether cos(θ-60)+cos(θ+60)=cos(θ) is True

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prove cos(θ-60)+cos(θ+60)=cos(θ)

prove

cos (θ - 6 0^{\circ}) + cos (θ + 6 0^{\circ}) = cos (θ)

True

Solution steps

cos (θ - 6 0^{\circ}) + cos (θ + 6 0^{\circ}) = cos (θ)

Manipulating left side

cos (θ - 6 0^{\circ}) + cos (θ + 6 0^{\circ})

Rewrite using trig identities

= \frac{1}{2} cos (θ) + \frac{3}{2} sin (θ) + cos (θ + 6 0^{\circ})

Rewrite using trig identities

= \frac{1}{2} cos (θ) + \frac{3}{2} sin (θ) + \frac{1}{2} cos (θ) - \frac{3}{2} sin (θ)

Simplify

\frac{1}{2} cos (θ) + \frac{3}{2} sin (θ) + \frac{1}{2} cos (θ) - \frac{3}{2} sin (θ) : cos (θ)

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

tan (2 A) = \frac{2 tan ( A )}{1 - tan ^{2} ( A )}

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

sec^{2} (x) - sec^{2} (x) cos^{2} (x) = tan^{2} (x)

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

\frac{2}{tan ( x ) + cot ( x )} = sin (2 x)

Is cos(θ-60)+cos(θ+60)=cos(θ) ?
The answer to whether cos(θ-60)+cos(θ+60)=cos(θ) is True