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Question
Select the correct option from the given alternatives:
`tan"A"/(1 + sec"A") + (1 + sec"A")/tan"A"` is equal to
Options
2cosecA
2secA
2sinA
2cosA
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Solution
2cosec A
Explanation:
`tan"A"/(1 + sec"A") + (1 + sec"A")/tan"A"`
= `(tan^2"A"+1+sec^2"A"+2sec"A")/((1+sec"A")tan"A")`
= `(sec^2"A"+sec^2"A"+2sec"A")/((1+sec"A")tan"A")` ......[∵ 1 + tan2A = sec2A]
= `(2sec"A"(sec"A"+1))/((1+sec"A")tan"A")=(2sec"A")/(tan"A")`
= `2/(sin"A")` = 2cosecA
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