Is sin^2(pi/4-2pi)=cos^2(pi/4-2pi) ?

The answer to whether sin^2(pi/4-2pi)=cos^2(pi/4-2pi) is True

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prove sin^2(pi/4-2pi)=cos^2(pi/4-2pi)

prove

sin^{2} (\frac{π}{4} - 2 π) = cos^{2} (\frac{π}{4} - 2 π)

True

Solution steps

sin^{2} (\frac{π}{4} - 2 π) = cos^{2} (\frac{π}{4} - 2 π)

Manipulating left side

sin^{2} (\frac{π}{4} - 2 π)

Rewrite using trig identities

= (\frac{2}{2})^{2}

(\frac{2}{2})^{2} = \frac{1}{2}

= \frac{1}{2}

Manipulating right side

cos^{2} (\frac{π}{4} - 2 π)

Rewrite using trig identities

= (\frac{2}{2})^{2}

(\frac{2}{2})^{2} = \frac{1}{2}

= \frac{1}{2}

We showed that the two sides could take the same form

\Rightarrow True

sec (θ) = tan (θ) csc (θ)

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

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

csc^{3} (x) + csc^{2} (x) + csc (x) = csc (x)

1 - 8 sin^{2} (x) cos^{2} (x) = cos (4 x)

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