what is x for tan23x=2sin23x

Selena Cowan

Selena Cowan

Answered

2022-01-23

what is x for tan23x=2sin23x

Answer & Explanation

trasahed

trasahed

Expert

2022-01-24Added 14 answers

tan23x=2sin23x
tan23x2sin23x=0
sin23x(1cos23x2)=0
sin23x(sec23x2)=0
So we have either
sin23x=0
3x=0,180,360
x=0,60,120
or
sec23x2=0
sec23x=2
sec3x=±2
3x=45,135,225,315
x=15,45,75,105
From the above, the only admissible solutions are 15,45,60,75
The sum of these angles is 195
Allison Compton

Allison Compton

Expert

2022-01-25Added 16 answers

Do some trigonometry and find the general solution first:
tan23x=2sin23x=2tan23x1+tan23xtan23x(1+tan23x)=2tan23x
So,
either tan3x=03x0 mod 180x0 mod 60;
or tan23x=1tan3x=±13x±45 mod 180x±15 mod 60
Then select the values in [0,90]

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