If $sin(60-x)-sin(60-x)=0$ what is $x$ ?

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Answer 1 · 2017-02-22T14:36:53

$x=kpi, k in ZZ$

$sin(60-x)-sin(60-x)=0$
So
$sin(60-x)-sin(60-x)=-sin(x)$
$rarr -sin(x)=0$
$rarr sin(x)=0$ which is true for $x=0$ and all integer multiples of $pi$ .

Answer 2 · 2017-02-22T14:42:13

Perhaps you mean $sin (60-x)-sin(60+x)=-sinx$ . Please see below for solution.

Perhaps you mean $sin (60-x)-sin(60+x)=-sinx$

As $sinC-sinD=2cos((C+D)/2)sin((C-D)/2)$

Hence $sin (60-x)-sin(60+x)=2cos((60-x+60+x)/2)sin((60-x-60-x)/2)$

= $2cos60sin(-x)$

= $2xx1/2xx(-sinx)$

= $-sinx$

If sin(60-x)-sin(60-x)=0sin(60-x)-sin(60-x)=0 what is xx?