Question
Download Solution PDFSimplify : \(\rm \frac{\cos A}{1+\tan A}-\frac{\sin A}{1+\cot A}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\rm \frac{\cos A}{1+\tan A}-\frac{\sin A}{1+\cot A}\)
Concept used:
a2 - b2 = (a + b)(a - b)
Calculation:
\(\rm \frac{\cos A}{1+\tan A}-\frac{\sin A}{1+\cot A}\)
⇒ \(\rm \frac{\cos A}{1+\frac{\sin A}{\cos A}}-\frac{\sin A}{1+\frac{\cos A}{\sin A}}\)
⇒ \(\rm \frac{\cos A}{\frac{\cos A+ \sin A}{\cos A}}-\frac{\sin A}{\frac{\sin A+\cos A}{\sin A}}\)
⇒ \(\rm \frac{\cos ^2A}{{\cos A+ \sin A}}-\frac{\sin^2 A}{{\sin A+\cos A}}\)
⇒ \(\rm \frac{\cos ^2A -\sin ^2A }{{\cos A+ \sin A}}\)
⇒ \(\rm \frac{{(\cos A+ \sin A})({\cos A- \sin A})}{{\cos A+ \sin A}}\)
⇒ cos A - sin A
∴ The required answer is cos A - sin A.
Last updated on Jul 9, 2025
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