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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)  -...

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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

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