Question

Attach HAND WRITTEN Answer to the question


QUESTION:

cosA-sinA+1
-------------------- = cosecA + cotA
cosA+sinA-1


Attach hand written answer

Answer 1

$\bf\huge LHS = \frac{cosecA - sinA + 1}{cosA + sinA - 1}$

Divide numerator and denominator with sinA

= $\bf\huge\frac{cotA - 1 + cosecA}{cotA + 1 - cosecA}$

= $\bf\huge\frac{cotA + cosecA - 1}{1 - cosecA + cotA}$

= $\bf\huge\frac{(cotA + cosecA) - (cosec^2A - cot^2A}{1 - cosecA + cotA)}$

= $\bf\huge\frac{(cotA + cosecA) - (cosecA + cotA)(cosecA - cotA}{1 - cosecA + cotA}$

= $\bf\huge\frac{(cosecA + cotA)(1 - cosecA + cotA)}{1 - cosecA + cotA}$

= cosecA + cotA

LHS = RHS