Question

Pls answer to this quickly.... Make me a doubtless person on this qtn....

Answer 1

Answer:

$\text{ L.H.S. } \frac{cos A - sin A + 1}{cos A + sin A - 1}$

Dividing both numerator and denominator by sin A,

$\implies \frac{cot A - 1 + cosec A}{cot A + 1 - cosec A}$

$\implies \frac{cot A - (cosec^2 A - cot^2) + cosec A}{cot A + 1 - cosec A}$

$\implies \frac{cot A - (cosec A + cot)(cosec A - cot A) + cosec A}{cot A + 1 }$

$\implies \frac{(cot A + cosec A) - (cosec A + cot)(cosec A - cot A) }{cot A + 1 - cosec A}$

$\implies \frac{(cot A + cosec A)[1 - (cosec A - cot A)]}{cot A + 1 - cosec A}$

$\implies \frac{(cot A + cosec A)(1 - cosec A + cot A)}{cot A + 1 - cosec A}$

$\implies cot A + cosec A=\text{ R.H.S.}$