Tīpoka ki ngā ihirangi matua
Kimi Pārōnaki e ai ki θ
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Tohaina

\frac{\mathrm{d}}{\mathrm{d}\theta }(\frac{\cos(\theta )}{\sin(\theta )})
Whakamahia te tautuhinga o te pātapa taupoki.
\frac{\sin(\theta )\frac{\mathrm{d}}{\mathrm{d}\theta }(\cos(\theta ))-\cos(\theta )\frac{\mathrm{d}}{\mathrm{d}\theta }(\sin(\theta ))}{\left(\sin(\theta )\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(\theta )\left(-\sin(\theta )\right)-\cos(\theta )\cos(\theta )}{\left(\sin(\theta )\right)^{2}}
Ko te pārōnaki o sin(\theta ) ko cos(\theta ), me te pārōnaki o cos(\theta ) ko −sin(\theta ).
-\frac{\left(\sin(\theta )\right)^{2}+\left(\cos(\theta )\right)^{2}}{\left(\sin(\theta )\right)^{2}}
Whakarūnātia.
-\frac{1}{\left(\sin(\theta )\right)^{2}}
Whakamahia te Tuakiri Pythagorean.
-\left(\csc(\theta )\right)^{2}
Whakamahia te tautuhinga o te aho taupoki.