cos^2a + cos^2b=2 then tan^2a + cot^2b=?
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The expression (1) is:
Cos^2b - Sin^2b = (1 - sin^2a + cos^2a)/(1 + sin^2a - cos^2a) But sin^2a + cos^2a = 1
Cos^2b - Sin^2b = (1 - (1-cos^2a) + cos^2a)/(1 + sin^2a - (1-sin^2a))
Cos^2b - Sin^2b = 2 cos^2a/ 2 sin^2a = 1/cot^2a
Cos^2b - Sin^2b = (1 - sin^2a + cos^2a)/(1 + sin^2a - cos^2a) But sin^2a + cos^2a = 1
Cos^2b - Sin^2b = (1 - (1-cos^2a) + cos^2a)/(1 + sin^2a - (1-sin^2a))
Cos^2b - Sin^2b = 2 cos^2a/ 2 sin^2a = 1/cot^2a
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