1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Domain and Range of Basic Inverse Trigonometric Functions
If sin-1 x...
Question
If
(
sin
−
1
x
+
sin
−
1
w
)
(
sin
−
1
y
+
sin
−
1
z
)
=
π
2
, then
D
=
∣
∣
∣
x
N
1
y
N
2
z
N
3
w
N
4
∣
∣
∣
(
N
1
,
N
2
,
N
3
,
N
4
ϵ
N
)
A
has a maximum value of 2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
has a minimum value of 0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
16 different D are possible
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
has a minimum value of -2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct options are
A
has a maximum value of 2
C
16 different D are possible
D
has a minimum value of -2
(
sin
−
1
x
+
sin
−
1
w
)
(
sin
−
1
y
+
sin
−
1
z
)
=
π
2
⇒
sin
−
1
x
+
sin
−
1
w
=
sin
−
1
y
+
sin
−
1
z
=
π
or
sin
−
1
x
+
sin
−
1
w
=
sin
−
1
y
+
sin
−
1
z
=
−
π
⇒
x
=
y
=
w
=
z
=
1
or
x
=
y
=
w
=
z
=
−
1
Hence, the maximum value of
∣
∣
∣
1
N
1
1
N
2
1
N
3
1
N
4
∣
∣
∣
=
∣
∣
∣
1
−
1
1
1
∣
∣
∣
=
2
and minimum value
∣
∣
∣
−
1
1
1
1
∣
∣
∣
=
−
2
Also, there are 16 different determinants as each place value is either 1 or -1.
Suggest Corrections
0
Similar questions
Q.
If sin
−1
x + sin
−1
y + sin
−1
z =
3
π
2
, then write the value of x + y + z.
Q.
If
sin
-
1
x
+
sin
-
1
y
+
sin
-
1
z
+
sin
-
1
t
=
2
π
, then find the value of x
2
+ y
2
+ z
2
+ t
2
Q.
If
(
sin
−
1
x
+
sin
−
1
w
)
(
sin
−
1
y
+
sin
−
1
z
)
=
π
2
, then
D
=
∣
∣
∣
x
N
1
y
N
2
z
N
3
w
N
4
∣
∣
∣
(
N
1
,
N
2
,
N
3
,
N
4
ϵ
N
)
Q.
If
sin
−
1
x
+
sin
−
1
y
+
sin
−
1
z
=
3
π
2
, then find the minimum value of
x
2
+
y
2
+
z
2
Q.
If
sin
−
1
x
+
sin
−
1
y
+
sin
−
1
z
=
3
π
2
, then the value of
x
9
+
y
9
+
z
9
−
1
x
9
y
9
z
9
is equal to
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Basic Inverse Trigonometric Functions
MATHEMATICS
Watch in App
Explore more
Domain and Range of Basic Inverse Trigonometric Functions
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app