Inverse Trigonometric Functions Worksheets With Answers Page 5
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MATHEMATICS
tan
– sec
(– 2) = tan
– [π – sec
2]
–1
–1
–1
–1
3
3
Solution
π
π π
π
⎛ ⎞
1
2
–1
− π +
= −
+ = −
cos
⎜ ⎟
=
.
3
⎝ ⎠
2
3
3
3
3
–1
–1
sin
cos sin
Evaluate:
.
Example 7
2
3
π
1
π
–1
–1
–1
–1
sin
cos sin
sin
cos
sin
=
.
Solution
2
3
2
6
Prove that tan(cot
x) = cot (tan
x). State with reason whether the
–1
–1
Example 8
equality is valid for all values of x.
x = θ. Then cot θ = x
Let cot
–1
Solution
π
π
x =
tan
– θ =
–1
tan
– θ
⇒
or,
x
2
2
⎛
⎞
⎛
⎞
π
π
=
=
=
−
=
–1
–1
–1
tan(cot
) tan θ cot
– θ
cot
cot
cot(tan
)
So
⎜
⎟
⎜
⎟
x
x
x
⎝
2
⎠
⎝
2
⎠
x are true for x ∈ R.
The equality is valid for all values of x since tan
x and cot
–1
–1
⎛
⎞
y
–1
tan
Find the value of sec
⎜
⎟
.
Example 9
⎝
2
⎠
⎛
⎞
π π
y
y
–1
∈ −
tan
=θ
θ
,
Let
, where
⎜
⎟
. So, tanθ =
,
Solution
2
⎝
2 2
⎠
2
2
4
y
which gives
secθ=
.
2
+
2
⎛
⎞
4
y
y
–1
sec tan
= secθ =
Therefore,
⎜
⎟
.
⎝
2
⎠
2
8
–1
cos
Find value of tan (cos
x) and hence evaluate tan
.
–1
Example 10
17
x = θ, then cos θ = x, where θ ∈ [0,π]
Let cos
–1
Solution
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