Cosecant of Angle plus Right Angle

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Theorem

$\csc \left({x + \dfrac \pi 2}\right) = \sec x$


Proof

\(\ds \csc \left({x + \frac \pi 2}\right)\) \(=\) \(\ds \frac 1 {\sin \left({x + \frac \pi 2}\right)}\) Cosecant is Reciprocal of Sine
\(\ds \) \(=\) \(\ds \frac 1 {\cos x}\) Sine of Angle plus Right Angle
\(\ds \) \(=\) \(\ds \sec x\) Secant is Reciprocal of Cosine

$\blacksquare$


Also see


Sources