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 ) = 0My 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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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    )  =  0My 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?

dkmc4175fl · Accepted Answer

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

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?

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