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

tan (\frac{π}{4} - θ) = \frac{1 - tan ( θ )}{1 + tan ( θ )}

\frac{sin ( θ )}{cot ( θ ) + csc ( θ )} = 1 - cos (θ)

csc^{2} (x) cos^{2} (x) = cot^{2} (x)

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

1 + tan^{2} (θ) = \frac{1}{cos ^{2} ( θ )}

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