<span>y' = tg' x + ctg' x = 1/(cos^2 (x) ) + (- 1/(sin^2 (x) ) = 1/(cos^2 (x) ) - 1/(sin^2 (x) ) = 1/(sin^2 (x) * cos^2 (x) ) = [(1-cos(2x))/2 ]*[(1+cos(2x))/2] = (1-cos^2 (2x) )/4</span>
Sn=(a1+an)*n/2
75=(a1-7,5)*n/2
(a1-7,5)n=150
a1=an-d(n-1) = -7,5+2,5(n-1) =-7,5+2,5n-2,5 = 2,5n-10
(2,5n-10-7,5)n=150
2,5n²-17,5n-150=0
n²-7n-60=0
D=7²-4(-60)=49+240=289=17²
n=(7±17)/2=-5;12
-5<0
n=12
a1=2,5*12-10=30-10=20