Question

Please answer this question​

Answer 1

We are asked to solve the integral:

`{:\implies \quad \displaystyle \sf \int (dx)/(\cos^(2)(x)-\tan (x)\cos^(2)(x))}`

Re write as

`{:\implies \quad \displaystyle \sf \int \frac{dx}{\cos^(2)(x)\{1-\tan (x)\}}}`

Using (1/cos x) = sec(x), we have

`{:\implies \quad \displaystyle \sf \int (\sec^(2)(x)dx)/(1-\tan (x))}`

Now, substitute 1 - tan (x) = t, so that -dt = sec²(x) dx

`{:\implies \quad \displaystyle \sf -\int (1)/(t)dt}`

`t`

`{:\implies \quad \boxed+C}`

Where, C is any Arbitrary Constant