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Question
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Solution
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))`
= `sqrt((1 + sinq)/(1 - sinq) . (1+ sinq)/(1 + sinq)) + sqrt((1 - sinq)/(1 + sinq) . (1 - sinq)/(1 - sinq))`
= `sqrt((1 + sinq)^2/(1 - sin^2q)` + `sqrt((1 - sinq)^2/(1 - sin^2q))` = `sqrt((1 + sinq)^2/cos^2q)` + `sqrt((1 - sinq)^2/cos^2q)`
= `(1 + sinq)/cosq + (1 - sinq)/cosq = (1 + sinq + 1 - sinq)/cosq` = `2/cosq`
= 2 secq
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