Question

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Answer 1

Answer:

see attachment :)

Step-by-step explanation:

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Answer 2

Answer:

To prove,

$\frac{1 + sinx}{cosx} = \frac{1 + sinx + cosx}{1 + cosx - sinx}$

Calculations,

$RHS = \frac{1 + cosx + sinx}{1 + cosx - sinx} \\ = \frac{1 + cosx + sinx}{1 + cosx - sinx} \times \frac{1 + cosx + sinx}{1 + cosx + sinx} \\ = \frac{ {(1 + cosx + sinx)}^{2} }{ {(1 + cosx)}^{2} - {sin}^{2}x } \\ = \frac{1 + 2cosx + {cos}^{2}x + 2sinx + 2sinxcosx + {sin}^{2} x}{1 + 2cosx + {cos}^{2} x - {sin}^{2}x } \\ = \frac{1 +sinx + cosx + sinxcosx }{cosx(1 + cosx)} \\ = \frac{1}{cosx} + \frac{1}{1 + sinx} + \frac{sinx}{1 + sinx} \\ = \frac{1}{cosx} + 1 \\ = \frac{1 + sinx}{cosx} \\ = LHS$

hence ,

$\frac{1 + sinx}{cosx} = \frac{1 + sinx + cosx}{1 + cosx - sinx}$