Find general solutions for 2tanx - cotx + 1 = 0
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Answer:
General Solution of the given equation is and x = nπ + 3π/4
Step-by-step explanation:
Given Equation,
2 tan x - cot x + 1 = 0
To find: General Solution of the given equation.
Consider,
2 tan x - cot x + 1 = 0
2 tan x - 1/tan x + 1 = 0
2 tan² x - 1 + tan x = 0
2 tan² x + tan x - 1 = 0
2 tan² x + 2 tan x - tan x - 1 = 0
2 tan x ( tan x + 1 ) - ( tan x + 1 ) = 0
( 2tan x - 1 ) ( tan x + 1 ) = 0
⇒ 2 tanx - 1 = 0 and tan x + 1 = 0
⇒ tan x = 1/2 and tan x = -1
⇒ and tan x = tan 3π/4
⇒ and x = 3π/4
We know that when tan x = tan y
the general solution is given by , x = nπ + y
Here,
and x = nπ + 3π/4
Therefore, General Solution of the given equation is and x = nπ + 3π/4
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