Trigonometry equation simplification So, I've been given the trig equation: csc^2 x−cot^2 x=1 Using the identity and rearranging cot^2 2x+1=csc^2 2x the equation simplifies to cot^2 2x−cot 2x=0

Demarion Ortega

Demarion Ortega

Answered question

2022-11-04

Trigonometry equation simplification
So, I've been given the trig equation:
csc 2 x cot 2 x = 1
Using the identity and rearranging
cot 2 2 x + 1 = csc 2 2 x
the equation simplifies to
cot 2 2 x cot 2 x = 0
factoring out cot 2 x
cot 2 x ( cot 2 x 1 ) = 0
I've bee told to solve x | 0 x 180
So...
cot 2 x = 0
or
cot 2 x = 1
1 tan 2 x = 0 1 = 0 × tan 2 x
therefore no solutions.
cot 2 x = 1 tan 2 x = 1
x { 22.5 , 112.5 }
Both of my solutions were correct, but I lost marks since apparently there are two extra solutions! 45 & 135 degrees. I don't know where I went wrong in my workings and was wondering if someone could tell me what I did wrong.

Answer & Explanation

Miah Carlson

Miah Carlson

Beginner2022-11-05Added 17 answers

cot 2x = 0
cot 2x = cot 90
As cot 90 = 0
2x = 90
x = 45
So x { 45 , 135 }

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