Extraneous solutions without performing squaring operation Solve in

palmantkf4u

palmantkf4u

Answered question

2022-04-03

Extraneous solutions without performing squaring operation
Solve in [0. 2π]
secx+tanx=2cosx

Answer & Explanation

Cassius Villarreal

Cassius Villarreal

Beginner2022-04-04Added 11 answers

Step 1
Note that this is not limited to trigonometric equations.
You obtained sec(x)tan(x)=12cos(x) by taking the inverse of both sides of the equation.
Let examine the very simple case x=2d1x=d12
Notice that when summing these two equations
x+d1x=d52
you now end up with two solutions 2 and 12
This happens because you symmetrized the equation to S(x,1x)=0 therefore whenever x is solution, 1x is solution too and the extraneous 12 appears.
This is more or less the same issue here, but of course because we are dealing with trigonometric functions, the extraneous solutions are not just the inverses, but the principle is the same.
Cecilia Nolan

Cecilia Nolan

Beginner2022-04-05Added 13 answers

Step 1
Subtract the two equation to find
2tanx=2cosxd12cosx
As cosx0
multiply out both sides by 2cosx, to find
4sinx=4cos2x1=4(1sin2x)1
Your solution needs to satisfy this equation as well

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