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Question
`int 1/(sin x * cos x)` dx = ?
Options
log |sin x| + c
log |cos x| + c
log |tan x| + c
log |sec x| + c
MCQ
Solution
log |tan x| + c
Explanation:
`int 1/(sin x * cos x)` dx
`= int (sin^2x + cos^2x)/(sin x * cos x) dx`
`= int [(sin^2x)/(sin x cos x) + (cos^2x)/(sin x cos x)]`dx
= ∫(tan x + cot x)dx
= log |sec x| + log |sin x| + c
= log |sec x × sin x| + c
= log |tan x| + c
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Trigonometric Equations and Their Solutions
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