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Find the absolute value of: sec (pi/7)+sec (3pi/7)+sec (5pi/7)

Find the absolute value of: sec (pi/7)+sec (3pi/7)+sec (5pi/7)

Grade:11

1 Answers

Vikas TU
14149 Points
9 months ago
Dear student 
Dear student 
cos(π/7) + cos(3π/7) + cos(5π/7)  
Multuiply and divide by 2sin(π/7)  
= 1/2sin(π/7) [ 2sin(π/7)cos(π/7) + 2sin(π/7)cos(3π/7) + 2sin(π/7)cos(5π/7) ]  
Use the following  
sin(2A) = 2sinAcosA  
2sinAcosB = sin(A+B) + sin(A-B)  
= 1/2sin(π/7) [ sin(2π/7) + sin(π/7+3π/7) + sin(π/7-3π/7) + sin(π/7+5π/7) + sin(π/7-5π/7) ]  
= 1/2sin(π/7) [ sin(2π/7) + sin(4π/7) + sin(-2π/7) + sin(6π/7) + sin(-4π/7) ]  
= 1/2sin(π/7) [ sin(2π/7) + sin(4π/7) - sin(2π/7) + sin(6π/7) - sin(4π/7) ]  
= 1/2sin(π/7) [sin(6π/7)]  
= 1/2sin(π/7) [sin(π - π/7)]  
= [sin(π/7)]/2sin(π/7)  
= 1/2

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