3tan²a+10tana+3=0
(3tana+1)(tana+3)=0
-1
[5sin²α/2+(8sinα/2)cosα/2+11cos²α/2-8]÷(√2)sin(α-π/2)
=[5+4sinα+6cos²α/2-8]÷(√2)sin(α-π/2)
=[4sinα+6cos²α/2-3]÷(-√2)cosα
=[4sinα+3cosα]÷(-√2)cosα
=-4sinα/√2cosα-3cosα/√2cosα
=-4√2sinα/2cosα-3√2cosα/2cosα
=-2√2sinα/cosα-3√2/2
=-2√2tana-3√2/2
=-2√2*(-1/3)-3√2/2
=3√2/2-3√2/2
=0