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The value of lim( x rarr 0) [ln(1 + sin^...

The value of `lim_( x rarr 0) [ln(1 + sin^2 x) cot ln^2 (1+x)]` is :

Text Solution

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`lim_(x->0)(ln(1+sin^2x))/(tan(ln(1+x))`
multiplying and dividing by `Sin^2x`
`lim_(x->0) sin^2x/((tan(ln^2(1+x))/ln^2(1+x))`
`lim_(x->0)sin^2x/((ln(1+x))^2`
multiplying and dividing by `x^2`
`lim_(x->0)(sinx/x)^2/((ln(1+x))^2/x`
`1/1=1`.
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