Question

Prove that
SinA - cosA+1/sinA+cosA-1=cosA/1-sinA
Please answer it with clear steps

Answer 1

welcome to the concept of trignometry

trignometry formulas used:

$1 + tan {}^{2} a = sec {}^{2} a$

and

$si n {}^{2} a + cos {}^{2} a = 1$

and algebra formula :

$a {}^{2} - b { }^{2} = (a - b)(a + b)$

first solve LHS then problem become easy .....

I hope my answer help you ✌️✌️.

Mark answer as brainlist ❤️

Answer 2

$\frac{sina - cosa + 1}{sina + cosa - 1} \\ \\ = \frac{ \frac{sina - cosa + 1}{cosa} }{ \frac{sina + cosa - 1}{cosa} } \\ \\ = \frac{tana + seca - 1}{tana - seca + 1} \\ \\ = \frac{tana + seca - 1}{( {sec}^{2} a - {tan}^{2}a) - (seca - tana) } \\ \\ = \frac{tana + seca - 1}{(seca - tana)(seca + tana - 1)} \\ \\ = \frac{1}{seca - tana} \\ \\ = \frac{1}{ \frac{1 - sina}{cosa} } \\ \\ = \frac{cosa}{1 - sina}$