tan A tanl + tana cota
IfA+B = 90. prove that
sin? B
cosA
tana
sta seca
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A + B = 90° => A = 90 - B
So Tan A = Cot (90 - A) = Cot B
So Tan B = Cot (90 - B) = Cot A
SecB = Cosec (90 -B) = Cosec A
CosA = Sin (90 -A) = Sin B
substitute these in the LHS,
TanA\ TanB+\frac{TanA\ CotB}{SinA \ SecB}-\frac{Sin^2B}{Cos^2A}\\\\=TanA\ CotA + \frac{TanA\ TanA}{SinA\ CosecA}-\frac{Sin^2B}{Sin^2B}\\\\=1+Tan^2A - 1=Tan^2A
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