Is cos(x+pi)cos(x-pi)=cos^2(x) ?

The answer to whether cos(x+pi)cos(x-pi)=cos^2(x) is True

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prove cos(x+pi)cos(x-pi)=cos^2(x)

prove

cos (x + π) cos (x - π) = cos^{2} (x)

True

Solution steps

cos (x + π) cos (x - π) = cos^{2} (x)

Manipulating left side

cos (x + π) cos (x - π)

Rewrite using trig identities

= cos (x + π) (- cos (x))

Rewrite using trig identities

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

Simplify

(- cos (x)) (- cos (x)) : cos^{2} (x)

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) + \frac{cos ( θ )}{tan ( θ )} = csc (θ)

(1 + tan^{2} (u)) (1 - sin^{2} (u)) = 1

sec^{3} (x) = \frac{1}{cos ^{3} ( x )}

sin (x) = \frac{5}{13}

sec (x) - tan (x) \cdot sin (x) = \frac{1}{sec ( x )}

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