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Question
Evaluate the following limit.
`lim_(x -> 0) (cosec x - cot x)`
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Solution
`lim_(x → 0) (cosec x - cot x)`
= `lim_(x → 0) (1/sinx - cosx/sinx)`
= `lim_(x → 0) (1 - cosx)/sinx xx sinx/sinx`
= `lim_(x → 0) ((1 - cosx). sinx)/((1 - cosx)(1 + cosx))`
= `lim_(x → 0) ((sinx)/(1+ cosx))`
= `0/2`
= 0
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