Question

integral 1 - sin x by cos square x dx

Answer 1

hope u get the solution

Answer 2

Answer:

$\tan x-\sec x+C$

Step-by-step explanation:

The given integral is $\int \frac{\left(1-sinx\right)}{cos^2x}$

Expand the given integral as shown below

$\int \frac{1}{\cos ^2\left(x\right)}-\frac{\sin \left(x\right)}{\cos ^2\left(x\right)}dx$

This, can be rewritten as

$\int (\sec^2x-\sec x\tan x)dx$

Apply the sum formula of integral: $\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$\int \sec^2x dx-\int\sec x\tan x dx$

Apply the common formula for integral, we get

$\tan x-\sec x+C$