Question

If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is ______.

Options

• `nπ ± π/8`

• `nπ ± π/4`

• `nπ ± π/3`

• `nπ ± π/2`

Answer 1

If `tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0, then the general value of x is `underlinebb(nπ ± π/3)`.

Explanation:

`tanx/(tan 2x) + (tan 2x)/tanx + 2` = 0

Put `tanx/(tan 2x)` = t

∴ `t + 1/t + 2` = 0

∴ t² + 2t + 1 = 0

∴ (t + 1)² = 0

∴ t + 1 = 0

∴ t = –1

`\implies tanx/(tan 2x)` = –1

∴ `(tanx * (1 - tan^2x))/(2tanx)` = –1

∴ 1 – tan²x = –2

`\implies` tan²x = 3

∴ tan x = `sqrt(3)`

`\implies` x = `tan^-1 sqrt(3) = pi/3`

∴ x = `nπ ± π/3`