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Cos 20.cos100 plus cos100.cos140 minus cos140.cos200 is equal to

Cos 20.cos100  plus cos100.cos140 minus cos140.cos200   is   equal   to
 
 

Grade:11

2 Answers

Arun
25750 Points
3 years ago
cosA + cosB = 2[cos(A + B)/2][cos(A - B)/2]
 
i.e. (1/2)(cosA + cosB) = [cos(A + B)/2][cos(A - B)/2]
 
=> cos20cos100 = (1/2)(cos120 + cos80)
 
=> cos100cos140 = (1/2)(cos240 + cos40)
 
=> -cos140cos200 = -(1/2)(cos340 + cos60)
 
=> (1/2)[cos120 + cos80 + cos240 + cos40 – cos340 – cos60]
 
=> (1/2)[-1/2 + cos80 – 1/2 + cos40 – cos340 – 1/2]
 
=> (1/2)[-3/2 + cos80 + cos40 – cos340]
 
=> (1/2)[-3/2 + 2cos60cos20 – cos340]
 
=> (1/2)[-3/2 + cos20 – cos340]
 
=> (1/2)[-3/2 + cos20 – cos(-20)]
 
So, (1/2)(-3/2) = -3/4
Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
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