Is cos(2((7pi)/4)-pi/2)=-1 ?

The answer to whether cos(2((7pi)/4)-pi/2)=-1 is True

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prove cos(2((7pi)/4)-pi/2)=-1

prove

cos (2 (\frac{7 π}{4}) - \frac{π}{2}) = - 1

True

Solution steps

cos (2 \cdot \frac{7 π}{4} - \frac{π}{2}) = - 1

Manipulating left side

cos (2 \frac{7 π}{4} - \frac{π}{2})

Rewrite using trig identities

= - 1

We showed that the two sides could take the same form

\Rightarrow True

sin (4 5^{\circ} + a) = sin (4 5^{\circ} - a)

1 - (1 - sin (x)) = sin (x)

\frac{- cos ( x )}{sin ( x )} = cot (x)

sin (- \frac{2 π}{5}) = - sin (\frac{2 π}{5})

sin (θ) - tan (θ) = \frac{sin ( θ )}{1 - cos ( θ )}

Is cos(2((7pi)/4)-pi/2)=-1 ?
The answer to whether cos(2((7pi)/4)-pi/2)=-1 is True