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