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5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined. cos A/(1+sin A) + (1+sin A)/cos A = 2 sec A

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one month ago Anand Kumar Pandey
1583 Points
```							Dear Student(cos A/(1+sin A)) + ((1+sin A)/cos A) = 2 sec A Now, take the L.H.S of the given equation.L.H.S. = (cos A/(1+sin A)) + ((1+sin A)/cos A)= [cos2A + (1+sin A)^2]/(1+sin A)cos A= (cos^2 A + sin^2 A + 1 + 2sin A)/(1+sin A) cos ASince cos^2 A + sin^2 A = 1, we can write it as= (1 + 1 + 2sin A)/(1+sin A) cos A= (2+ 2sin A)/(1+sin A)cos A= 2(1+sin A)/(1+sin A)cos A= 2/cos A = 2 sec A = R.H.S.L.H.S. = R.H.S.(cos A/(1+sin A)) + ((1+sin A)/cos A) = 2 sec AHence proved.Thanks
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one month ago
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