How do you solve #Sin x + Sin 2x + Sin 3x + Sin 4x = 0#?
2 Answers
In this way, using the sum-to-product formula for sinus and cosine:
So:
Then:
Reminder of Concept to solve trig equations:
To solve a complex trig equation, transform it into a few basic trig equations. Solving trig equations finally results in solving basic trig equations.
In this example of solving: f(x) = sin x + sin 2x + sin 3x + sin 4x = 0, use the trig identity of "sin a + sin b" to transform f(x) into a product of 3 basic trig equations like Massimiliano finely did:
Next, solve separately the 3 basic trig equations: cos x = 0, sin