Buktikan bahwa Tan-1 x + Tan-1 y = Tan-1 ( (x + y) / ( 1 – xy) )

Penyelesaian:

Untuk membuktikan

Tan⁻¹x + Tan⁻¹y = Tan⁻¹( (x + y) /( 1 – xy))

Mari kita pertimbangkan LHS

Tan⁻¹x + Tan⁻¹y = M

Mengambil Tan kedua sisi

Tan M = Tan (Tan⁻¹x + Tan⁻¹y )

Tan(A + B) = (Tan A + Tan B)/(1 – TanA TanB)

A = Tan⁻¹x & B =Tan⁻¹y

Tan M = [Tan(Tanx) + Tan( Tan⁻¹y)]/[1 – Tan(Tan⁻¹x)Tan(Tan⁻¹y)]

Tan M = (x + y) /(1 – xy)

M = Tan⁻¹[(x + y) /(1 – xy)]

M = Tan⁻¹x + Tan⁻¹y = RHS

Tan⁻¹x + Tan⁻¹y = Tan⁻¹[(x + y)/( 1 – xy)]

10