what is the limit of the function (1-sin x)/cos^2 x, x -> 90 degrees?

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We have to find the value of lim x--> 90[ (1- sin x)/(cos x)^2]

substituting x = 90 degrees, we get the indeterminate form 0/0, so we can use l'Hopital's rule and substitute the numerator and denominator by their derivatives.

=> lim x->90 [ (- cos x)/ (-2 cos x * sin x)]

=> lim x->90 [ 1/ (2 sin x)]

substitute x = 90

=> 1/ 2

The required value of lim x--> 90[ (1- sin x)/(cos x)^2] is (1/2).

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