Question

cot2x+cotx=3 please help me with this
help sos
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Answer 1

Given    Cot 2x +  Cot x = 3.      Solve for x.

we know Tan2x =  2 tanx / (1 - tan² x)
So             Cot 2x = (1-tan² x) / (2 tan x)

Now   (1 - tan²x) / (2 tanx)  + 1/tanx  = 3
          1 - tan² x + 2 = 6 tan x
          tan² x + 6 tan x - 3 = 0
            Tan x = [ -6 +- √48 ] /2  = -3 + - 2√3

So x = 24.89°   or   204.89°   or  98.79° or  278.79°

Answer 2

★ TRIGONOMETRIC REDUCTIONS ★

Given equation is : Cot 2x + Cot x = 3

Tan 2x = 2tanx / 1 - tan² x

Cot 2x = 1 - Tan² x / 2Tan x

Now inverting ;

1 - Tan² x / 2Tanx = 3

Tan²x + 6 Tanx - 3 = 0

Now , it's a quadratic in Tanx ... which can be reduced more further,

Hence , after reducing , we obtain the roots in quadratic Tanx as ;

Tanx = -6 ± √48 / 2

= -3 ± 2√3

Or aslike ,

x = Tan^-1 ( -3 ± 2√3 )

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