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Question
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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Solution
L.H.S
`cos A/(1 + sin A) + (1 + sin A)/cos A `
= `(cos^2A+(1+sinA)^2)/((1+sinA)(cosA))`
= `(cos^2A + 1+sin^2A + 2sinA)/((1+sinA)(cosA))`
= `(sin^2+cos^2A+1+2sinA)/((1+sinA)(cosA))`
= `(1+1+2sinA)/((1+sinA)(cosA))`
= `(2+2sinA)/((1+sinA)(cosA))`
= `(2(1+sinA))/((1+sinA)(cosA))`
= `2/(cosA)`
= 2 secA
= R.H.S
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