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Ngā Raru Ōrite mai i te Rapu Tukutuku

Tohaina

\frac{\mathrm{d}}{\mathrm{d}t}(\frac{\cos(t)}{\sin(t)})
Whakamahia te tautuhinga o te pātapa taupoki.
\frac{\sin(t)\frac{\mathrm{d}}{\mathrm{d}t}(\cos(t))-\cos(t)\frac{\mathrm{d}}{\mathrm{d}t}(\sin(t))}{\left(\sin(t)\right)^{2}}
Mō ngā pānga e rua e taea ana te pārōnaki, ko te pārōnaki o te otinga o ngā pānga e rua ko te tauraro whakareatia ki te pārōnaki o te taurunga tango i te taurunga whakareatia ki te pārōnaki o te tauraro, ā, ka whakawehea te katoa ki te tauraro kua pūruatia.
\frac{\sin(t)\left(-\sin(t)\right)-\cos(t)\cos(t)}{\left(\sin(t)\right)^{2}}
Ko te pārōnaki o sin(t) ko cos(t), me te pārōnaki o cos(t) ko −sin(t).
-\frac{\left(\sin(t)\right)^{2}+\left(\cos(t)\right)^{2}}{\left(\sin(t)\right)^{2}}
Whakarūnātia.
-\frac{1}{\left(\sin(t)\right)^{2}}
Whakamahia te Tuakiri Pythagorean.
-\left(\csc(t)\right)^{2}
Whakamahia te tautuhinga o te aho taupoki.