prove that 4cos12.cos48.cos72=cos36
Answers
Answered by
2
4cos12
o
cos48
o
cos72
o
=2(2cos12
o
cos48
o
)cos72
o
=2[cos(12+48)+cos(12−48)]cos72
o
=2[cos60
o
+cos36
o
]cos72
o
=2cos60
o
cos72
o
+2cos36
o
cos72
o
=2×
2
1
cos72
o
+[(cos36+72)+cos(36−7)]
=cos72
o
+cos108
o
+cos36
o
=2cos(72
o
+108
o
)/2cos(72
o
−108
o
)/2+cos36
o
=2cos90
o
cos18
o
+cos36
o
=cos36
o
[∵cos90
o
=0].
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