Find ∫cosect−$$1dt$$

Correct option is 1logsint+12+sin2t+sint+c

Questions

$Find \int \sqrt{cosect - 1} d t$

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detailed solution

Correct option is A

∫cosect−1dt=∫1−sintsintdt=∫1−sint1+sintsint(1+sint)dt Use =∫1y2−a2=log⁡y+y2−a2+c=∫cos⁡tsin2⁡t+sin⁡tdt Put sin⁡t=y=∫dyy2+y=∫dyy+122−122+c=log⁡y+12+y2+y+c=log⁡sin⁡t+12+sin2⁡t+sin⁡t+c

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Find ∫cosect−1dt

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$Find \int \sqrt{cosect - 1} d t$