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

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

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

prove

sin (z + \frac{π}{2}) = cos (z)

True

Solution steps

sin (z + \frac{π}{2}) = cos (z)

Manipulating left side

sin (z + \frac{π}{2})

Rewrite using trig identities

= cos (z)

We showed that the two sides could take the same form

\Rightarrow True

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2 csc (2 x) = csc (x) sec (x)

cos (\frac{π}{4}) = \frac{2}{2}

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

sec^{2} (x) - tan (x) cot (x) = tan^{2} (x)