tan(-105) find the value of it
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Step-by-step explanation:
Find tan (105)
Ans:
1
+
√
3
1
−
√
3
Explanation:
tan (105) = sin (105)/cos (105). Find sin 105 and cos 105.
Apply the trig identity: sin (a + b) = sin a.cos b + sin b.cos a
sin (105) = sin (60 + 45) = sin 60.cos 45 + sin 45.cos 60 =
=
(
√
3
2
)
(
√
2
2
)
+
(
√
2
2
)
(
1
2
)
=
(
√
2
4
)
(
1
+
√
3
)
cos (105) = cos (60 + 45) = cos 60.cos 45 - sin 60.sin 45 =
=
(
1
2
)
(
√
2
2
)
−
(
√
3
2
)
(
√
2
2
)
=
(
√
2
4
)
(
1
−
√
3
)
tan
105
=
sin
cos
=
1
+
√
3
1
−
√
3
Check by calculator.
sin 105 = - 3.74
1
+
√
3
1
−
√
3
=
2.73
−
0.73
=
−
3.74
. OK
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