The equation is \(\displaystyle\sqrt{{{3}+{4}{{\cos}^{{2}}{\left({x}\right)}}}}={\frac{{{\sin{{\left({x}\right)}}}}}{{\sqrt{{{3}}}}}}+{3}{\cos{{\left({x}\right)}}}\)

Guadalupe Glass

Guadalupe Glass

Answered question

2022-03-31

The equation is
3+4cos2(x)=sin(x)3+3cos(x)

Answer & Explanation

Cody Hart

Cody Hart

Beginner2022-04-01Added 11 answers

The roots of 4t233t3 are 34 and 3
A slightly different approach to this problem could be the following:
3+4cos2(x)sin2(x)363sin(x)cos(x)9cos2(x)
=13(33sin(2x)7cos(2x)+1)
With this we have
33sin(2x)+7cos(2x)=219sin(2x+y)
where y=arcsin7219. Hence the roots can be found as
x=12(arcsin1219arcsin7219)+2πn
x=arcsin1219+arcsin7219+2πn
now note that
arcsin1219+arcsin7219=arcsin(1219172192+7219112192}
=arcsin32
=π3
Further using tan(α+β) and tan(arcsinx)=x1x2 we obtain
arcsin1219arcsin7219=2arctan34

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?