Question

integration .....
prove it​

Answer 1

It's too simple

Use tanx = sinx / cosx

- sinx = d (cos x) / dx

Integral tanx dx

= Integral (sinx / cosx) dx

= Integral { [ - d (cos x) / dx ] / cos x } dx

Put cosx = u

= - Integral du / u

= - ln | u | + C

= ln 1 / | u | + C

= ln 1 / | cosx | + C

= ln | sec x | + C

I have done indefinite integration

Now put the limit of integration yourself

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Answer 2

Answer:

tanx = sinx / cosx

- sinx d (cosx) / dx

= Integral (sinx / cosx) dx

= Integral [{- d (cosx) / dx} / cosx] dx

put cosx = u

= - Integral du / u

= - In l u l + C

= In 1 / l u l + C

= In 1 / l cosx l + C

= In l sinx l + C

Then put the limit of integration.

Hope it helps.