Question

Solve sin3x + sinx/cosx + cos3x= tan2x

Trigonometric equation and identitie
ANSWERED
asked 2020-11-05
Solve \(\displaystyle{\sin{{3}}}{x}+\frac{{\sin{{x}}}}{{\cos{{x}}}}+{\cos{{3}}}{x}={\tan{{2}}}{x}\)

Answers (1)

2020-11-06
\(\displaystyle{\sin{{A}}}+{\sin{{B}}}={2}{\sin{{\left(\frac{{{A}+{B}}}{{2}}\right)}}}{\cos{{\left(\frac{{{A}-{B}}}{{2}}\right)}}},\)
\(\displaystyle{\cos{{A}}}+{\cos{{B}}}={2}{\cos{{\left(\frac{{{A}+{B}}}{{2}}\right)}}}{\cos{{\left(\frac{{{A}-{B}}}{{2}}\right)}}}.\)
If A=3x and B=x, \(\displaystyle{\sin{{3}}}{x}+{\sin{{x}}}={2}{\sin{{2}}}{x}{\cos{{x}}},{\cos{{3}}}{x}+{\cos{{x}}}={2}{\cos{{2}}}{x}{\cos{{x}}}.\)
Therefore \(\displaystyle\frac{{{\sin{{3}}}{x}+{\sin{{x}}}}}{{{\cos{{x}}}+{\cos{{3}}}{x}}}={2}{\sin{{2}}}{x}\frac{{\cos{{x}}}}{{2}}{\cos{{2}}}{x}{\cos{{x}}}={\tan{{2}}}{x}\)
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-01-19
Verify this triganomic identity you can only use 1 side to solve \(\displaystyle\frac{{{\cos{{x}}}-{\tan{{x}}}}}{{{\sin{{x}}}+{\cos{{x}}}}}={\cos{{x}}}-{\sec{{x}}}\)
asked 2020-12-30
Solve \(\displaystyle{\left({1}+{\cos{{x}}}\right)}\frac{{\tan{{x}}}}{{2}}={\sin{{x}}}\)
asked 2020-12-28

simplify \((\cos x/1+\sin x)+(1+\sin x/\cos x)\)

asked 2020-11-01
Simplify the expression \(\displaystyle\frac{{\sec{{x}}}}{{\sin{{x}}}}-\frac{{\sin{{x}}}}{{\cos{{x}}}}\)
asked 2020-10-18
If \(\displaystyle{\sin{{x}}}+{\sin{{y}}}={a}{\quad\text{and}\quad}{\cos{{x}}}+{\cos{{y}}}={b}\) then find \(\displaystyle{\tan{{\left({x}-\frac{{y}}{{2}}\right)}}}\)
asked 2021-01-28
Verify the identity \(\displaystyle\frac{{\cos{{x}}}}{{1}}-{\sin{{x}}}-{\tan{{x}}}=\frac{{1}}{{\cos{{x}}}}\)
asked 2021-05-29
tan(x)+√3=0
asked 2021-06-02
If J is jointly proportional to G and V, and J = √3 when G = √2 and V = √8, what is J when G = √6 and V = 8?
asked 2021-05-09
Find the altitude of an isosceles triangle with base 4.24 feet. The vertex angle of the triangle measures 85°
asked 2021-05-31
Understand sine and cosine values on the unit circle Question
If the terminal side of angle tt goes through the point \(\displaystyle{\left(-{\left(\frac{{5}}{{13}}\right)},-{\left(\frac{{12}}{{13}}\right)}\right.}\) on the unit circle, then what is cos(t)?
Provide your answer below: \(\displaystyle{\cos{{\left({t}\right)}}}=□\)
...