Simplify cosA/1+sinA + 1+sinA/cosA
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Answer:
Given, cos A/1+sin A+1+sin A/cos A
Step-by-step explanation:
=cos^2 A+1+sin^2 A/(1+sin A)cos A (LCM of 1+sin A and cos A)
=cos^2 A+sin^2 A+1/(1+1/cosec A)cos A
=1+1/(cosec A+1/cosec A)cos A
=2/cos A cosec A+cos A/cosec A
=2/cos A 1/sin A+cos A/cosec A
=2/cos A+sin A cos A/sin A/cosec A
=2/cos A/sin A+sin A cos A/sin A/cosec A
=2/cot A+cos A/cosec A
=2 X cosec A/cot A+cos A
=2cosec A/cot A+cos A
=2cosec A/cot A+cosec A/sec A
=1/2sin A/cos A/sin A+cosec A/sec A
=1/ sin A/cos A+1/ sin A/1/cos A
=1/tan A+1/sin A X cos A
=cot A+cos A/sin A
=cot A+cot A
=2 cot A
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