Question

cosec A-1/ cosec A +1 ( rationalise the denominator)​

Answer 1

$\frac{(cosecA-1)}{(cosecA+1)} \\= \frac{(cosecA-1)(cosecA-1)}{(cosecA+1)(cosecA-1)} \\= \frac{(cosecA-1)^{2}}{cosec^{2}A- 1^{2}} \\= \Big(\frac{cosecA-1}{cotA}\Big)^{2} \\= \Big(\frac{\frac{1}{SinA}-1}{\frac{cosA}{sinA}}\Big)^{2} \\= \Big(\frac{\frac{1-sinA}{SinA}}{\frac{cosA}{sinA}}\Big)^{2} \\= \Big( \frac{1-sinA}{cosA}\Big)^{2}\\= \Big(\frac{1}{cosA} - \frac{sinA}{cosA}\Big)^{2} \\= (secA-tanA)^{2}$

Therefore.,

$\red{ \frac{(cosecA-1)}{(cosecA+1)} }$

$\green { = (secA-tanA)^{2} }$

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