cotA+tanB/cotB+tanA=cotA×tanB prove
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multiply the numerator and denominator of the LHS by tanA.tanB
we get (tanB+tanA.tan²B)/( tanA + tan²A.tanB )
take tanB common from numerator and tanA from denominator.
we get tanB(1+tanAtanB)/tanA(1+tanAtanB)
as we can see 1+tanAtanB cancels out
leaving us with tanB/tanA and hence corAtanB
we get (tanB+tanA.tan²B)/( tanA + tan²A.tanB )
take tanB common from numerator and tanA from denominator.
we get tanB(1+tanAtanB)/tanA(1+tanAtanB)
as we can see 1+tanAtanB cancels out
leaving us with tanB/tanA and hence corAtanB
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