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If sec(A-2B), secA, sec(A+2B) are in A....

If `sec(A-2B), secA, sec(A+2B)` are in A.P. then value of `(Cos^(2)A)/(Cos^(2)B)` is less than:

A

1

B

`(1)/(2)`

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
`2 secA= sec (A-2B) +Sec (A+2B)`
`(2)/(cosA)=(2cos A cos 2B)/(cos^(2)A-sin^(2)(2B))`
`cos^(2)A- sin^(2)(2B)=cos^(2)A cos2B`
`cos^(2)A(1-cos2B)= sin^(2)(2B)`
`cos^(2)A2sin^(2)B=4 sin^(2)cos^(2)B`
`(cos^(2)A)/(cos^(2)B)=2`
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