What can you deduce from cosX(A−B)=0? So this is the problem: sin2x=sqrt(2)cos x cosx(2sinx−sqrt(2)=0 My question is, how can I come with this to the conclusion that, according to my answer sheet, cosx=0 and sinx=sqrt(2)/2 Is it just plugging in something until it works?

Sariah Mcguire 2022-10-15 Answered
What can you deduce from cos X ( A B ) = 0?
So this is the problem:
sin 2 x = 2 cos x
cos x ( 2 sin x 2 ) = 0
My question is, how can I come with this to the conclusion that, according to my answer sheet, cos x = 0 and sin x = 2 2 Is it just plugging in something until it works?
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Answers (1)

dkmc4175fl
Answered 2022-10-16 Author has 15 answers
Recall in Algebra you solved problems like ( x 2 ) ( x + 3 ) = 0? So for my example you get x 2 = 0 or x + 3 = 0, and solve.
For your equation, we have ( cos x ) ( 2 sin x 2 ) = 0. We use the Zero Product Property to get cos x = 0 or 2 sin x 2 = 0. This second equation, upon solving for sin x, results in sin x = 2 / 2
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