Prove that tan*sin *(cos+1) + cosx= sin^2 x + sec x

tanx*sinx* (cosx+1) + cosx = sin62 x+ sec
x

Let us start from the left side and prove the right
side.

We know that tanx =
sinx/cosx

==> sinx/cosx * sinx ( cosx+ 1) +
cosx

==> We will rewrite using the common
denominator.

==> (sin^2x ( cosx+1) + cos^2 x) /
cosx

==> (sin^2 x * cosx + sin62 x + cos^2 x) /
cosx

But sin^2 x + cos^2 x =
1

==> (sin^2 x *cosx + 1 ) /
cosx

==> sin^2 x cosx/ cosx + 
1/cosx

==> sin^2 x + sec x
.............q.e.d

Then we have prove that :
tanx*sinx(cosx+1) + cosx = sin^2 x + sec x