1.

Please solve it fast question 5 it is ncert question

Answer» HEY there !!


▶ PROVE that :-

\frac{ \cos A - \sin A \: + 1 }{\cos A + \sin A \: - 1} = cosecA + \cot A . \\ \\


▶ SOLUTION :-

Solving LHS .

→ DIVIDING numerator and denominator by sin A .

= \frac{ \frac{ \cos A}{ \sin A} - \cancel\frac{ \sin A}{ \sin A} + \frac{1}{ \sin A} }{\frac{ \cos A}{ \sin A} + \cancel\frac{ \sin A}{ \sin A} - \frac{1}{ \sin A} } \\ \\ = \frac{ \cot A - 1 + cosecA}{ \cot A + 1 - cosecA} . \\ \\ = \frac{( \cot A + cosecA) - ( {cosec}^{2} A - { \cot}^{2}A) }{ \cot A + 1 - cosecA } \\ \\ = \frac{( \cot A + cosecA) - (cosecA + \cot A)(cosecA - \cot A)}{ \cot A + 1 - cosecA} . \\ \\ = \frac{( \cot A + cosecA) \cancel{(1 - cosecA + \cot A)}}{ \cancel{( \cot A + 1 - cosecA)} }. \\ \\ = \huge \boxed{ \green{ \cot A + cosecA.}}



✔✔ HENCE, it is proved ✅✅.



THANKS



#BeBrainly.


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