已知tan(π⼀4+a)=1⼀2则sin2a-cos2a=多少

2024-11-23 08:01:09

推荐回答（1个）

回答1：

解：由已知tan(π/4
+
a)
=
[tan(π/4)
+
tana]/[1
–
tan(π/4)tana]
=
(1
+
tana)/(1
–
tana)
=
1/2，去分母得2(1
+
tana)
=
1
–
tana，展开可得2
+
2tana
=
1
–
tana，移项得3tana
=
-1，所以tana
=
-1/3
；
原式
=
sin2a
–
cos2a
=
2sinacosa
–
(cos
2
a
–
sin
2
a)
=
sin
2
a
+
2sinacosa
–
cos
2
a
=
(sin
2
a
+
2sinacosa
–
cos
2
a)/(sin
2
a
+
cos
2
a)
=
(tan
2
a
+
2tana
–
1)/(tan
2
a
+
1)
=
[(-1/3)
2
+
2*(-1/3)
–
1]/[(-1/3)
2
+
1]
=
(1/9
–
2/3
–
1)/(1/9
+
1)
=
(1
–
6
–
9)/(1
+
9)
=
-14/10
=
-7/5
。
综上所述，sin2a
–
cos2a
=
-7/5
。