If ,
[tex] \cot(A) + \csc(A) = 2[/tex]
Then show that
[tex] \frac{ \sin(A) - \cos(A) + 1 }{sin(A) + cos(A )- 1} = \frac{2 \cos(A) }{1 - \cos(A) } [/tex]
[tex] \cot(A) + \csc(A) = 2[/tex]
Then show that
[tex] \frac{ \sin(A) - \cos(A) + 1 }{sin(A) + cos(A )- 1} = \frac{2 \cos(A) }{1 - \cos(A) } [/tex]
Answers & Comments
Answer:
To show the given expression:
\[ \frac{\sin(A) - \cos(A) + 1}{\sin(A) - \cos(A) + 1} \]
is equal to
\[ \frac{2 \cos(A)}{1 - \cos(A)} \]
you can start by manipulating the given expression. Multiply both the numerator and denominator by the conjugate of the denominator, which is \( \sin(A) + \cos(A) - 1 \):
\[ \frac{\sin(A) - \cos(A) + 1}{\sin(A) - \cos(A) + 1} \times \frac{\sin(A) + \cos(A) - 1}{\sin(A) + \cos(A) - 1} \]
Simplify the expression, and you should be able to reach the desired form. If you encounter any issues or need further assistance, feel free to ask.