# Prove sin x tan x = sec x - cos x

### 2 Answers | Add Yours

sin(x)*tan(x) = sec(x) - cos(x)

We will start from the left side.

==> We know that tan(x) = sin(x)/cos(x)

==> sin(x)*tan(x) = sin(x)*sin(x)/ cos(x)

= sin^2 x/ cos(x)

But we know that sin^2 x = 1- cos^2 x

==> sin(x)*tan(x) = (1-cos^2 x) / cosx

= 1/cos(x) - cos^2 x / cosx

But 1/cosx = sec(x)

**==> sin(x)*tan(x) = sec(x) - cos(x).........q.e.d**

L:H:S ≡ sin x tan x

= sinx (sinx/cosx)

= sin²x/cosx

= (1-cos²x)/cosx

= 1/cosx - cos²x/cosx

= secx - cosx

= R:H:S