Asked by ceasar
Given that A + B = 120 degrees and cosA + cos B = 1 divided by squareroot of 2,show that cos A-B divided by 2 = 1 divided by square root of 2
Answers
Answered by
Reiny
Hope you have come across this formula:
cosA + cosB = 2cos[(A+B)/2]cos[(A-B)/2]
from A+B = 120°
(A+B)/2 = 60°
cos[(A+B)/2] = cos 60° = 1/2
so in the above equation....
1/√2 = 2(1/2)cos[(A-B)/2]
cos[(A-B)/2] = 2(1/√2) / (1/2) = 1/√2
cosA + cosB = 2cos[(A+B)/2]cos[(A-B)/2]
from A+B = 120°
(A+B)/2 = 60°
cos[(A+B)/2] = cos 60° = 1/2
so in the above equation....
1/√2 = 2(1/2)cos[(A-B)/2]
cos[(A-B)/2] = 2(1/√2) / (1/2) = 1/√2
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