Is cos(z)=sin(pi/2+z) ?

The answer to whether cos(z)=sin(pi/2+z) is True

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prove cos(z)=sin(pi/2+z)

prove

cos (z) = sin (\frac{π}{2} + z)

True

Solution steps

cos (z) = sin (\frac{π}{2} + z)

Manipulating right side

sin (\frac{π}{2} + z)

Rewrite using trig identities

= cos (z)

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (θ) (2 + cot^{2} (θ)) = 1

- cos^{2} (2 θ) = \frac{1 + cos ( 4 θ )}{8}

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

tan (- \frac{π}{2} - θ) = cot (θ)

\frac{( 1 + tan ( θ ) )}{( 1 + cot ( θ ) )} = tan (θ)