If cos2A=tan^2B then show that cos2B=tan^2A

 Steps to  prove that If cos2A=tan^2B then show that cos2B=tan^2A

Given that

cos2A=tan^2B

L.H.S

=cos2B

[cos2A=1-tan^2A/1+tan^2A]

=1-tan^2B/1+tan^2B

=1-cos2A/1+cos2A [Given that  cos2A=tan^2B]

[1-cos2A=2sin^A]

[1+cos2A=2cos^A]

=2sin^2A/2cos^2A

=tan^2A

=R.H.S

Hence If cos2A=tan^2B then shows that cos2B=tan^2A is proved.

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