Prove that, Prove that, tanA + 2tan2A + 4tan4A + 8cot8A = cotA 8cot8A = cotA
tan(2X) = 2tan(X)/{1 – tan^2(X)} ---------------------------------------------------- (1)
LHS
tanA + 2tan2A + 4tan4A + 8{1 – tan^2(4A)}/2tan(4A), using (1)
tanA + 2tan2A + {8tan^2(4A) + 8 – 8tan^2(4A)}/2tan(4A)
tanA + 2tan2A + 4/tan(4A)
tanA + 2tan2A + 4{1 – tan*2(2A)}/2tan(2A), using (1)
tanA + {4tan^2(2A) + 4 – 4tan*2(2A)}/2tan(2A)
tanA + 2/tan(2A)
tanA + 2{1 – tan^2(A)}/2tan(A), using (1)
{2tan^2(A) + 2 – 2tan^2(A)}/2tan(A)
1/tan(A) = cot(A) = RHS