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Byju's Answer
Standard XII
Mathematics
Circular Measurement of Angle
If cos4Acos...
Question
If
cos
4
A
cos
2
B
+
sin
4
A
sin
2
B
=
1
, then
cos
4
B
cos
2
A
+
sin
4
B
sin
2
A
=
1
.
A
True
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B
False
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Solution
The correct option is
A
True
Given
cos
4
A
cos
2
B
+
sin
4
A
sin
2
B
=
1
⟹
cos
4
A
sin
2
B
+
sin
4
A
cos
2
B
=
cos
2
B
sin
2
B
⟹
(
1
−
sin
2
A
)
2
sin
2
B
+
sin
4
A
(
1
−
sin
2
B
)
=
(
1
−
sin
2
B
)
sin
2
B
⟹
sin
2
B
(
1
+
sin
4
A
−
2
sin
2
A
)
+
sin
4
A
−
sin
4
A
sin
2
B
=
sin
2
B
−
sin
4
B
⟹
sin
2
B
+
sin
4
A
sin
2
B
−
2
sin
2
A
sin
2
B
+
sin
4
A
−
sin
4
A
sin
2
B
−
sin
2
B
+
sin
4
B
=
0
⟹
sin
4
A
+
sin
4
B
−
2
sin
2
A
sin
2
B
=
0
⟹
(
sin
2
A
−
sin
2
B
)
2
=
0
⟹
sin
2
A
=
sin
2
B
⟹
cos
2
A
=
cos
2
B
cos
4
A
cos
2
B
+
sin
4
A
sin
2
B
=
1
⟹
(
cos
2
A
)
2
cos
2
B
+
(
sin
2
A
)
2
sin
2
B
=
1
⟹
cos
4
B
cos
2
A
+
sin
4
B
sin
2
A
=
1
So the given relation is
True
Suggest Corrections
0
Similar questions
Q.
If (cos⁴A/cos²B) + (sin⁴A/sin²B) = 1
Prove that
(cos⁴B/cos²A) + (sin⁴B/sin²A) = 1
Q.
Check whether the statement is true/false.
If
cos
4
A
cos
2
B
+
sin
4
A
sin
2
B
=
1
, then
sin
4
A
+
sin
4
B
=
2
sin
2
A
sin
2
B
.
Q.
If
cos
2
A
cos
2
B
+
sin
4
A
sin
2
B
=
1
, then show that
cos
2
A
cos
2
B
+
sin
4
A
sin
2
B
=
1
.
Q.
cos
2
B
−
cos
2
A
sin
2
A
+
sin
2
B
=
tan
(
A
−
B
)
Q.
If
cos
4
A
cos
2
B
+
sin
4
A
sin
2
B
=
1
, then which of the following is/are correct?
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