Problem 9 Easy Difficulty

Find the general solution for each of the following equations:
$$
\sin x+\sin 3 x+\sin 5 x=0
$$

Answer

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Precalculus

NCERT Class 11 - Math

Chapter 3

Trigonometric Functions

Section 4

Trigonometric Functions of Sum and Difference of Two Angles

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Video Transcript

the question is given Synnex plus sign three eggs plus sign five packs equal to zero. So here we have to find the general solutions. So you can write like that Sign X. Plus sign five X. Plus signed three X equal to zero. So here we have a formula for saying A plus sign B equal to two times sane april is be upon to times. Of course E. Negative be up on two. So now you can see that here we applied that formula and we get two times Sign explosive. Five facts upon to times goes Xnegative five X Upon to plus sign three X equal to zero. So here we get two times saying three X times goes two eggs plus sign three X equal to zero. Now we take common Synnex science reacts or times two times cause to eggs plus one equal to zero. So here are forced cast gas is signed, three acts equal to zero. Oh two times goes two acts plus one equal to zero, signed three acts equal to zero than general solution is three acts equal to and pie. So now we have to divide both sides by three. So here we get X equal to and by upon three where me an element of said that is a indigenous and it is a general solution in case second you can write like that cause to eggs eagle two negative one up on two. So here we know that of course 5.3 equal to one upon to. So now we put here goes to eggs equal to negative of course 5.3. So now goes to buy two eggs equal to of course by negative 5.3. Because here we know that in the second quarter in course will be negative. So now the general solution is to X equal to two times and by plus minus to buy upon three. So now we have to divide both sides by two. So here we get X equals do, and by plus minus 5.3 where an element of said. So our general solutions are X equal to end pipe on three, and X equals do, and by plus minus 5.3, so it is our final.

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