Question

(ii) tan x +tan 2x + tan x tan 2x = 1​

Answer 1

Solution : We have to find x.

Now, tanx + tan2x + tanx tan2x = 1

⇒ tanx + tan2x = 1 - tanx tan2x

⇒ (tanx + tan2x)/(1 - tanx tan2x) = 1

⇒ tan(x + 2x) = tan(π/4)

⇒ 3x = π/4

⇒ x = π/12

∴ the required solution is x = π/12.

Trigonometric rules :

tan(A + B) = (tanA + tanB)/(1 - tanA tanB)

tan(π/4) = 1