Question

((cotA+cosA-1)/(cotA-cosecA+1))=(1+cosA)/sinA

Answer 1

Hey there !!


→ Your question have some error:-

➡ You have written,


$\frac{ ( cotA + \underline{cosA} - 1 )}{ ( cotA - cosecA + 1 )} = \frac{ ( 1 + cosA )}{sinA} .$


→ The underlined part is wrong.


➡ The correct form will be :-


$\frac{ ( cotA + \underline{cosecA} - 1 )}{ ( cotA - cosecA + 1 )} = \frac{ ( 1 + cosA )}{sinA} .$


→ Solution :-

$\boxed{ \bf{see \: the \: attachment.}}$

$\large \boxed{ \bf \mathbb{TRIGONOMETRY.}}$

$\huge \bf \underline{ \mathbb{LHS = RHS.}}$



✔✔ Hence, it is proved ✅✅.

____________________________________



$\huge \boxed{ \mathbb{THANKS}}$


$\huge \bf{ \#BeBrainly.}$

Answer 2

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

$= cosecA + cotA \\ \\ = \frac{1 + cosA}{sinA}$