Is cos(-pi/4-5t)=cos(5t+pi/4) ?

The answer to whether cos(-pi/4-5t)=cos(5t+pi/4) is True

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prove cos(-pi/4-5t)=cos(5t+pi/4)

prove

cos (- \frac{π}{4} - 5 t) = cos (5 t + \frac{π}{4})

True

Solution steps

cos (- \frac{π}{4} - 5 t) = cos (5 t + \frac{π}{4})

Manipulating left side

cos (- \frac{π}{4} - 5 t)

Use the negative angle identity:

cos (- x) = cos (x)

= cos (\frac{π}{4} + 5 t)

= cos (5 t + \frac{π}{4})

We showed that the two sides could take the same form

\Rightarrow True

p ro v e tan (\frac{π}{4} - θ) = \frac{1 - tan ( θ )}{1 + tan ( θ )}

p ro v e cos^{2} (B) = \frac{1}{2} (1 + cos (2 B))

p ro v e sin (θ + π) = - sin (θ)

p ro v e sin (x + \frac{3 π}{2}) = - cos (x)

p ro v e sec (x) - sec (x) \cdot sin^{2} (x) = cos (x)

Is cos(-pi/4-5t)=cos(5t+pi/4) ?
The answer to whether cos(-pi/4-5t)=cos(5t+pi/4) is True