What is the value of tan 22.5
Answers
Answered by
4
Explanation:
Call tan (22.5) = tan t --> tan 2t = tan 45 = 1
Use trig identity:
tan
2
t
=
2
tan
t
1
−
tan
2
t
(1)
tan
2
t
=
1
=
2
tan
t
1
−
tan
2
t
-->
-->
tan
2
t
+
2
(
tan
t
)
−
1
=
0
Solve this quadratic equation for tan t.
D
=
d
2
=
b
2
−
4
a
c
=
4
+
4
=
8
-->
d
=
±
2
√
2
There are 2 real roots:
tan t = -b/2a +- d/2a = -2/1 + 2sqrt2/2 = - 1 +- sqrt2
Answer:
tan
t
=
tan
(
22.5
)
=
−
1
±
√
2
Since tan 22.5 is positive, then take the positive answer:
tan (22.5) = - 1 + sqrt2
Answered by
2
Answer:
hi,
root 2 -1
is your answer
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