x = cot 6° cot 42° and y= Tan66°Tan78° then
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Answer:
x
y
=tan6
0
tan42
0
tan66
0
tan78
0
=
cos6
∘
cos42
∘
cos66
∘
cos78
∘
sin6
∘
sin42
∘
sin66
∘
sin78
∘
=
(2cos66
∘
cos6
∘
)(2cos78
∘
cos42
∘
)
(2sin66
∘
sin6
∘
)(2sin78
∘
sin42
∘
)
=
(cos60
∘
+cos72
∘
)(cos36
∘
+cos120
∘
)
(cos60
∘
−cos72
∘
)(cos36
∘
−cos120
∘
)
=
(cos60
∘
+sin18
∘
)(cos36
∘
−sin30
∘
)
(cos60
∘
−sin18
∘
)(cos36
∘
+sin30
∘
)
=
(
2
1
+
4
5
−1
)(
4
5
−1
−
2
1
)
(
2
1
−
4
5
−1
)(
4
5
+1
+
2
1
)
=
(
5
+1)(
5
−1)
(3−
5
)(3+
5
)
=
5−1
9−5
=1
⇒y=x
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