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Sec(A+B) + Sec(A-B) = 2SecA then prove that cosa = +-2cosa/2

Sec(A+B) + Sec(A-B) = 2SecA then prove that cosa = +-2cosa/2

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Student
 
1/cos (A+B)  +  1/ cos (A-B) = 2 / cos A
cos (A+B) + cos (A-B) / (cos (A+B)cos(A –B))   = 2/ Cos A
 
2 cos A cos B = (cos (A+B)cos(A –B)) / cosA
cos2A cos B = (cos (A+B)cos(A –B)) 
cos2A cos B = cos2A – sin2B
cos2A (cos B – 1) = – sin2B
 
cos2A (cos B – 1) = (cos B – 1) (cos B +1) 
cos2A  = (cos B +1) 
cos2A  = 2 cos2(B/2) 
cosA = sqrt [2]* cos (B/2) 
 
Regards
Arun (askIITians forum expert)

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