Solve for x: sin x +sin 3x + sin 5x= 0

sinx+sin3x+sin5x=0

⇒(sin5x+sinx)+sin3x=0

⇒2sin3xcos2x+sin3x=0

⇒sin3x(2cos2x+1)=0

sin3x=0 or 2cos2x+1=0

sin3x=0 or, cos2x=−21

Now, sin3x=0⟹3x=nπ⟹x=3nπ,n∈Z

And, cos2x=−21

cos2x=cos32π

2x=2mπ±32π,m∈Z

x=mπ±3π,m∈Z

Hence, the general solution of the given equation is :

x=3nπ or, x=mπ±3π, where m,n∈Z

this question is given using the conditional form. conditional tenses are is used when talking about hypothetical situations and probabilities. also, this is used when making polite requests. so comprarías is the conjugation of the verb comprar that matches the second person singular in the conditional. finally:

¿cuál comprarías tú?