0 < a < pi ==> sina положителен
sin^2a + cos^2a = 1
sina = √(1 - cos^2a) = √(1 - 9/25) = 4/5 = 0,8
ctga = cosa/sina = 3/5*5/4 = 3/4 = 0,75
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1. В
2. sin^4a+sin^2acos^2a=sin^2a(sin^2a+cos^2a)=sin^2a*1=sin^2a
3. sin52cos38+cos52sin38=sin(52+38)=sin90=1
2011=n
2012=n+1
2011²+2011²·2012²+2012²=n^2+n^2*(n+1)^2+(n+1)^2=
=n^2+n^2*(n^2+2n+1)+(n^2+2n+1)=
=n^4+2n^3+3n^2+2n+1=
=n^2*(n^2+2n+3+2/n+1/n^2)=
=n^2*((n+1/n)^2+2(n+1/n)+1)=
=n^2*((n+1/n+1)^2)=
=(n^2+n+1)^2
2011²+2011²·2012²+2012²=(n^2+n+1)^2=(2011^2+2011+1)^2=<span>
4046133</span>^2