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Byju's Answer
Standard XII
Mathematics
Range of Trigonometric Expressions
If cos-1x #...
Question
If
cos
-
1
x
>
sin
-
1
x
, then
(a)
1
2
<
x
≤
1
(b)
0
≤
x
<
1
2
(c)
-
1
≤
x
<
1
2
(d) x > 0
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Solution
cos
-
1
x
>
sin
-
1
x
⇒
cos
-
1
x
>
π
2
-
cos
-
1
x
⇒
2
cos
-
1
x
>
π
2
⇒
cos
-
1
x
>
π
4
⇒
x
>
cos
π
4
⇒
x
>
1
2
We know that the maximum value of cosine fuction is 1.
∴
1
2
<
x
≤
1
Hence, the correct answer is option(a).
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