#Help me solve this limit please (no L'Hopital, no power series)

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ocean tartan
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I can't read your handwriting

spark wagon
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I assume the function is (sin(y + π/2)^2 - 1)/y? In that case:
(sin(y + π/2)^2 - 1)/y = (cos(y)^2 - 1)/y = -sin(y)^2/y
We know that sin(y)/y -> 1 as y -> 0. So:
-sin(y)^2/y = -sin(y)(sin(y)/y) -> -0*1 = 0, x -> 0
So, the limit is equal to 0.