Question

find cos ( a) /(1- tan a) + sin a/(1-cota)​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• $\sf \dfrac{\cos(a)}{1 - \tan(a)} + \dfrac{\sin(a)}{1 - \cot(a)}$

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• Value of $\sf \dfrac{\cos(a)}{1 - \tan(a)} + \dfrac{\sin(a)}{1 - \cot(a)}$

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Given that,

$\sf \dfrac{\cos(a)}{1 - \tan(a)} + \dfrac{\sin(a)}{1 - \cot(a)}$

Then,

$\\\sf = \dfrac{\cos(a)}{1 - \dfrac{\sin(a)}{\cos(a)}} + \dfrac{\sin(a)}{1 - \dfrac{\cos(a)}{\sin(a)}} \\\\ \sf = \dfrac{\cos(a)}{\dfrac{\cos(a) - \sin(a)}{\cos(a)}} + \dfrac{\sin(a)}{\dfrac{\sin(a) - cos(a)}{\sin(a)}} \\\\ \sf = \dfrac{\cos^{2}(a)}{\cos(a) - \sin(a)} + \dfrac{\sin^{2}(a)}{\sin(a) - \cos(a)} \\\\ \sf = \dfrac{\cos^{2}(a)}{\cos(a) - \sin(a)} - \dfrac{\sin^{2}}{\cos(a) - \sin(a)} \\\\ \sf = \dfrac{\cos^{2}(a) - \sin^{2}(a)}{\cos(a) - \sin(a)} \\\\ \sf = \dfrac{ \{\cos(a)- \sin(a)\}\{\cos(a) + \sin(a) \}}{\sin(a) - \cos(a)} \\\\ \sf = \cos(a) + \sin(a) \\\\ \sf = \sin(a) + \cos(a) \\\\ \sf$

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Answer 2

Step-by-step explanation:

si a + cos a proved....... ..