Question

cos A/1+tan A - sin A/1+cot A=?

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

The answer is $\cos A-\sin A$

Step-by-step explanation:

  $\displaystyle \frac{\cos A}{1+\tan A}-\frac{\sin A}{1+\cot A}$

$=\displaystyle \frac{\cos A}{1+\frac{\sin A}{\cos A}}-\frac{\sin A}{1+\frac{\cos A}{\sin A}}\\\\=\displaystyle \frac{\cos A}{\frac{\cos A+\sin A}{\cos A}}-\frac{\sin A}{\frac{\sin A+\cos A}{\sin A}}\\\\=\displaystyle \frac{\cos^2A}{\cos A+\sin A}-\frac{\sin^2A}{\sin A+\cos A}\\\\=\frac{\cos^2A-\sin^2 A}{\cos A+\\\sin A}=\frac{(\cos A+\sin A)(\cos A-\sin A)}{\cos A+\sin A}\\\\=\cos A-\sin A$