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Sec(45+a)sec(45-a)=2sec2a.plzz help me to prove this identity

Sec(45+a)sec(45-a)=2sec2a.plzz help me to prove this identity

Grade:11

3 Answers

Vikas TU
14149 Points
4 years ago
Taking L.H.S
Sec(45+a)sec(45-a)
=> 1/cos(45 + a)*cos(45 -a)
=> 1/(cos45cosa – sin45sina) (cos45cosa+sin45sina)
=> 2/(cosa -sina) (cosa + sina)
=> 2/(cos^2a -sin^2a)
=> 2/cos2a
=> 2sec2a
 
L..H.S = R.H.S
Varsha Jeyaraj
18 Points
4 years ago
=1/ cos(45+a) cos(45-a)=1/ (1/2 (cos90+cos2a)=1/ (1/2(0+cos2a)=1/ (0+1/2 cos2a )= 1/ (1/2 cos2a )=2/cos2a=2 sec2a
Varsha Jeyaraj
18 Points
4 years ago
L.H.S=1/ cos(45+a) cos(45-a)=1/ (1/2 (cos90+cos2a)=1/ (1/2(0+cos2a)=1/ (0+1/2 cos2a )= 1/ (1/2 cos2a )=2/cos2a=2 sec2a L.H.S=R.H.S

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