Question

prove that sec A-1/sec A+1 = 1-cos A/1+cos A

Answer 1

secA-1/secA+1=1/cosA-1/

Answer 2

Solution:

LHS =$\frac{secA-1}{secA+1}$

/* secA = 1/cosA */

= $\frac{\frac{1}{cosA}-1}{\frac{1}{cosA}+1}$

= $\frac{\frac{1-cosA}{cosA}}{\frac{1+cosA}{cosA}}$

After cancellation, we get

= $\frac{1-cosA}{1+cosA}$

= RHS

Therefore,

$\frac{secA-1}{secA+1}$ = $\frac{1-cosA}{1+cosA}$

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