What Steps Can Resolve a Trigonometric Equation Involving Sine and Cosine?

[chwala]

Homework Statement

[/B]
Solve $2sin3x.sinx=1$

Homework Equations

The Attempt at a Solution

I used the identity $( cos (A+B)= cos A cos B- sin A sin B), (cos(A-B) = cos A cos B+sinA sinB)→ -(cos 4x-cos2x)= 2sin 3xsinx, (cos 2x-cos4x=1)$now i am stuck , is this correct_
using $(cos 2x=2cos^2x-1)⇒(cos 4x=2cos^22x-1),→(2cos^22x-2cos^2x+1=0)$

is this correct, how do i move folks

 

[cnh1995]

I'd suggest you use the triple angle formula for sine. It will get much simpler.
Edit: No I think your current approach is good. Solve the quadratic equation using the discriminant method.

 

[ehild]

Homework Statement

[/B]
Solve $2sin3x.sinx=1$

Homework Equations

The Attempt at a Solution

I used the identity $( cos (A+B)= cos A cos B- sin A sin B), (cos(A-B) = cos A cos B+sinA sinB)→ -(cos 4x-cos2x)= 2sin 3xsinx, (cos 2x-cos4x=1)$now i am stuck , is this correct_
using ##(cos 2x=2cos^2x-1)⇒(cos 4x=2cos^22x-1),→(2cos^22x-2cos^2x+1=0)##

is this correct, how do i move folks

Substitute 2cos²(2x)-1 for cos(4x) into the equation cos(2x)-cos(4x)=1, and solve for cos(2x) .

 

[chwala]

Are you suggesting i use $sin 3x≡3sin x- 4sin^3x$

 

[chwala]

Substitute 2cos²(2x)-1 for cos(4x) into the equation cos(2x)-cos(4x)=1, and solve for cos(2x) .

Substitute 2cos²(2x)-1 for cos(4x) into the equation cos(2x)-cos(4x)=1, and solve for cos(2x) .

ehild hahahahahahahha that is what i was looking for lol, greetings from Africa bro

 

[cnh1995]

Are you suggesting i use sin3x≡3sinx−4sin3x

No.. I edited my previous post. I was talking about the approach in #3, but it looks like I misread your quadratic equation.

 

[chwala]

in that case i just have to solve $cos 2x(2cos 2x-1)=0$ thanks folks

 

[chwala]

I'd suggest you use the triple angle formula for sine. It will get much simpler.
Edit: No I think your current approach is good. Solve the quadratic equation using the discriminant method.

what do you mean by saying solve the quadratic using discriminant method...

 

[ehild]

ehild hahahahahahahha that is what i was looking for lol, greetings from Africa bro

grandma. :) You are welcome.

 

[cnh1995]

what do you mean by saying solve the quadratic using discriminant method...

Well, I read the equation wrong and thought it was a quadratic equation in 2x while it actually contains 2x as well as x. The discriminant method is used to solve quadratic equations. You can see it here.
https://www.google.co.in/url?sa=t&r...6iZeyqi0FPM0sYhcbjJ0_w&bvm=bv.139782543,d.c2I

 

[ehild]

Well, I read the equation wrong and thought it was a quadratic equation in 2x while it actually contains 2x as well as x. The discriminant method is used to solve quadratic equations.

The name is "quadratic formula" . Discriminant method is something different.