Question

prove that tan4x = 4tan(1-tan2x ÷ 1-6tan2x + tan4x​

Answer 1

Answer:

we know that tan2x=2tanx/1-tan^2x

so we can write tan4x as tan 2×(2x)

so by applying tan2x formula we will get

tan2(2x) =2tan2x/1-tan^2(2x)

again we got tan2x in the above eqn so again we will apply tan2x formula

tan2(2x) =[2{2tanx/1-tan^2x]/[1-{2tanx/1-tan^2x}^2]

={4tanx/1-tan^2x}/1-{4tan^2x/(1-tan^2x)^2}

=4tanx{1-tan^2x/1-6tan^2x+tan^4x}