Is sec(pi/2-u)=csc(u) ?

The answer to whether sec(pi/2-u)=csc(u) is True

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prove sec(pi/2-u)=csc(u)

prove

sec (\frac{π}{2} - u) = csc (u)

True

Solution steps

sec (\frac{π}{2} - u) = csc (u)

Manipulating left side

sec (\frac{π}{2} - u)

Rewrite using trig identities

= \frac{1}{sin ( u )}

Rewrite using trig identities

csc (u)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cot ^{3} ( t )}{csc ( t )} = cos (t) (csc^{2} (- 1))

\frac{sec ^{2} ( x ) cot ( x )}{csc ^{2} ( x )} = tan (x)

cot^{2} (x) - cos^{2} (x) cot^{2} (x) = cos^{2} (x)

cot (\frac{1}{x}) = cos (\frac{1}{x}) arcsin (\frac{1}{x})

\frac{tan ( x )}{sin ( x )} - sec (x) = 0