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Byju's Answer
Standard XII
Mathematics
Cos(A+B)Cos(A-B)
Find acute an...
Question
Find acute angles A and B, if
sin
(
A
+
2
B
)
=
√
3
2
and
cos
(
A
+
4
B
)
=
0
, and
A
>
B
.
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Solution
Given,
sin
(
A
+
2
B
)
=
√
3
2
cos
(
A
+
4
B
)
=
0
A
>
B
,
We know that,
sin
60
∘
=
√
3
2
and
cos
90
∘
=
0
Consider,
sin
(
A
+
2
B
)
=
√
3
2
and
sin
60
∘
=
√
3
2
⟹
(
A
+
2
B
)
=
60
∘
---------------(i)
Consider,
cos
(
A
+
4
B
)
=
0
and
cos
90
∘
=
0
⟹
(
A
+
4
B
)
=
90
∘
---------------(ii)
Solve (i) and (ii) :
(
A
+
2
B
)
=
60
∘
(
A
+
4
B
)
=
90
∘
Subtracting (i) from (ii),
2
B
=
30
∘
B
=
30
∘
2
=
15
∘
From (ii)
(
A
+
4
B
)
=
90
∘
Also,
B
=
15
∘
A
=
90
∘
−
60
∘
A
=
30
∘
∴
A
=
30
∘
,
B
=
15
∘
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Similar questions
Q.
Find acute angles A and B, if
sin
A
+
2
B
=
3
2
and
cos
A
+
4
B
=
0
,
A
>
B
.