Question

Please solve this..​

Answer 1

Answer:

$\int {\frac{dx}{cosx sin^{2}x}}$ = ln |sec x + tan x| - cosec x + C

Step-by-step explanation:

Given :- $\int {\frac{dx}{cosx sin^{2}x}}$

or $\int {\frac{1}{cosx sin^{2}x}} \, dx$

or $\int {\frac{sin^{2}x + cos^{2}x}{cosx sin^{2}x}} \, dx$                 {∵sin²x + cos²x = 1}

or $\int {[\frac{sin^{2}x}{cosx sin^{2}x} + \frac{cos^{2}x}{cosx sin^{2}x}}] \, dx$

or $\int {[\frac{1}{cosx} + \frac{cosx}{sin^{2}x}}] \, dx$

or $\int {[secx + cosecx.cotx] \, dx$

⇒ ln |sec x + tan x| - cosec x + C

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