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Step-by-step explanation:
If cos 2A = tan-B, then show that cos 2B = tan-A.
In ABC, prove that
cos A = 1/2 (See proof below)
[tex]cos(2A) = 2cos^{2} A-1[/tex]
Substitute cos 2A = -1/2 into the relationship above:
[tex]\frac{-1}{2} = 2cos^{2} A - 1\\\frac{-1}{2} + 1 = 2cos^{2} A\\\frac{1}{2} = 2cos^{2} A[/tex]
Divide both sides by 2:
[tex]\frac{1}{4} = cos^{2} A[/tex]
Square root both sides:
[tex]cosA = \sqrt{\frac{1}{4} } \\cosA = \frac{1}{2}[/tex]
Proved
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