Prove the Identity: tan(a)+tan(B)=(sin(a+B))/(cos(a)cos(B)

Question

a=Alpha

B=Beta

Answer 1

tan(a) + tan(b) = sin(a)/cos(a) + sin(b)/cos(b) the common denominator is cos(a)cos(b)

= sin(a)cos(b)/cos(a)cos(b) + sin(b)cos(a)/ cos(a)cos(b)

= (sin(a)cos(b) + sin(b)cos(a)) / cos(a)cos(b)

= sin(a + b) / cos(a)cos(b)

Answer 2

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