Question

sin ( 1+ tan ) + cos (1+ cot ) = sec + cosec

Answer 1

$sinx(1 + tanx) + cosx(1 + cotx) \\ = sinx + \frac{ {sin}^{2} x}{cosx} + cosx \\ + \frac{ {cos}^{2}x }{sinx} \\ = (sinx + \frac{ {cos}^{2}x }{sinx} ) + (cosx + \frac{ {sin}^{2}x }{cosx} ) \\ = \frac{ {sin}^{2}x + {cos}^{2}x }{sinx} + \frac{ {cos}^{2} x + {sin}^{2} x}{cosx} \\ = \frac{1}{sinx} + \frac{1}{cosx} \\ = cosec \: x + secx$

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