Question

已知1+tan(a+720°)/1-tan(a-360°)=3+2根号2求：

[cos²(π-a)+sin(π+a)cos(π-a)+2sin²(a-π)]1/cos²(-a-2π)的值

Answer 1

[1+tan(a+720°)/(1-tan(a-360°)]=3+2√2
(1+tana)/(1-tana)=3+2√2
(1+tana)=3+2√2(1-tana)
1+tana=(3+2√2)(1-tana)
1+tana=3+2√2-(3+2√2)tana
1+tana=3+2√2-3tana-2√2tana
2+2√2-4tana-2√2tana=0
1+√2-2tana-√2tana=0
1+√2-2tana-√2tana=0
2tana+√2tana=1+√2
√2tana(√2+1)=1+√2
√2tana=1
tana=√2/2

[cos²(π-a)+sin(π+a)cos(π-a)+2sin²(a-π)]1/cos²(-a-2π)
=[(-cosa)²+sinacosa+2(-sina)²]1/cos²a
=[cos²a+sinacosa+2sin²a]1/cos²a
=cos²a/cos²a+sinacosa/cos²a+sin²a/cos²a
=1+tana+tan²a
=1+√2/2+(√2/2)²
=1+√2/2+1/2
=√2/2+3/2