Inverse Trigonometric Functions Worksheets With Answers Page 6
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24INVERSE TRIGONOMETRIC FUNCTIONS
23
2
2
1 – cos θ
1 –
x
=
tan θ
=
.
Therefore,
tan(cos
x) =
–1
cosθ
x
2
⎛
8
⎞
1 –
⎜
⎟
⎛
⎞
⎝
17
⎠
8
15
Hence
.
=
–1
tan cos
=
⎜
⎟
8
⎝
17
⎠
8
17
–5
–1
sin 2cot
Find the value of
Example 11
12
⎛
⎞
–5
−
5
⎜
⎟
Let cot
= y . Then cot y =
.
–1
Solution
⎝
12
⎠
12
–5
–1
sin 2cot
Now
= sin 2y
12
⎡
⎤
⎛
⎞
12
–5
π
<
∈ ⎜
2
since cot
0, so
, π
⎟
⎢
y
y
⎥
= 2siny cosy
=
13
13
⎝
2
⎠
⎣
⎦
–120
169
1
4
–1
–1
cos sin
sec
Evaluate
Example 12
4
3
1
4
⎡
⎤
1
3
–1
–1
–1
–1
+
cos sin
sec
cos sin
cos
=
⎢
⎥
Solution
4
3
⎣
4
4
⎦
1
3
1
3
–1
–1
–1
–1
cos sin
cos cos
– sin sin
sin cos
=
4
4
4
4
2
2
3
1
1
3
1 –
–
1 –
=
4
4
4
4
3 15
1 7
3 15 – 7
–
=
.
4 4
4 4
16
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