Inverse Trigonometric Functions Worksheets With Answers Page 8
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24INVERSE TRIGONOMETRIC FUNCTIONS
25
⎛
⎞
3
1
+
⎜
⎟
11 18
3
1
–1
tan
⎜
⎟
–1
+
–1
tan
tan
=
=
(since xy < 1)
3
1
⎜
⎟
−
×
1
11
18
⎝
⎠
11 18
65
1
–1
–1
tan
tan
=
=
= cot
3
–1
195
3
Which is greater, tan 1 or tan
1?
–1
Example 15
From Fig. 2.1, we note that tan x is an increasing function in the interval
Solution
−π π
⎛
⎞
π
π
,
⎜
⎟
⇒ tan 1 > tan
, since 1 >
. This gives
⎝
2 2
⎠
4
4
Y
tan x
tan x
tan 1 > 1
π
⇒
tan 1 > 1 >
4
O
X
⇒
tan 1 > 1 > tan
–1
(1).
– /2
p – /2
p
p/4
p/4
p/2
p/2
Find the value of
Example 16
⎛
⎞
2
–1
–1
+
sin 2 tan
cos (tan
3)
⎜
⎟
.
⎝
3
⎠
2
2
Let tan
–1
= x and tan
–1
3 = y so that tan x =
and tan y =
3 .
Solution
3
3
⎛
2
⎞
–1
+
–1
sin 2 tan
cos (tan
3)
⎜
⎟
Therefore,
⎝
3
⎠
= sin (2x) + cos y
2
2.
1
2 tan
1
3
x
+
+
=
=
4
( )
2
+
1 tan
2
+
2
x
1 tan
+
1
+
y
1
3
9
12
1 37
+
=
=
.
13
2 26
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