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A+B+C=270° then cos2a+cos2b+cos2c+4sina sinb sinc Find the value

A+B+C=270° then cos2a+cos2b+cos2c+4sina sinb sinc
Find the value

Grade:12th pass

1 Answers

Harsh nadar
41 Points
2 years ago
Let's solve in different points by considering smaller units
Cos2a + Cos2b = 2Cos(a+b)Cos(a-b)
                            =2Cos(270-c)Cos(a-b)
                           =  -2Sin(c)Cos(a-b)
 
Cos2c = 1- 2Sin22c
 
4SinaSinbSinc = 2(2SinaSinb)Sinc
                          = 2[Cos(a-b) - Cos(a+b)]Sinc
                          = 2[Cos(a-b) - Cos(270-c)]Sinc
                          = 2[cos(a-b) + Sinc]Sinc
                          = 2Cos(a-b)Sinc + 2Sin2
now add the results of these three parts and get the desired 
ANS = 1
 
 
                   
 

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