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Question
`lim_(x -> pi/2) (1 - sin x)/cosx` is equal to ______.
Options
0
–1
1
Does not exit
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Solution
`lim_(x -> pi/2) (1 - sin x)/cosx` is equal to 0.
Explanation:
`lim_(x -> pi/2) (1 - sin x)/cosx`
= `lim_(y -> 0) (1 - sin pi/2 - y)/(cos pi/2 - y)` taking ` pi/2 - x = y`
= `lim_(y -> 0) (1 - cos y)/siny`
= `lim_(y -> 0) (2 sin^2 t/2)/(2sin y/2 cos y/2)`
= `lim_(y -> 0) tan y/2`
= 0
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