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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Compound Angles
what is tan14...
Question
what is tan142 1/2?
(mixed fraction)
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Solution
tan
142
.
5
=
tan
180
-
37
.
5
=
-
tan
37
.
5
Let 37.5 be x. Therefore,75 = 2x
tan
75
=
tan
2
x
=
2
tan
x
1
-
tan
2
x
1
-
tan
2
x
tan
75
=
2
tan
x
⇒
tan
75
tan
2
x
+
2
tan
x
-
tan
75
=
0
tan
x
=
-
2
±
4
+
4
tan
2
75
2
tan
75
=
-
1
±
1
cos
75
sin
75
cos
75
=
-
cos
75
±
1
sin
75
cos 75 = cos (45 + 30) =
3
-
1
2
2
and sin 75 = sin (45 + 30) =
3
+
1
2
2
Therefore, tan 37.5 =
1
-
3
+
2
2
3
+
1
as tan 37.5 > 0
Therefore, tan 142.5 = - tan 37.5 =
3
-
1
-
2
2
3
+
1
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