Question 23294
<pre>Solve: sin<sup>2</sup><i>x</i> = sin<i>x</i>cos<i>x</i>, 0 <font face = "symbol"><b>£</font> x < 2<font face = "symbol">p</font>
 
a. <i>x</i>=0, <font face = "symbol">p</font>/4
b. <i>x</i>=<font face = "symbol">p</font>/4, 5<font face = "symbol">p</font>/4
c. <i>x</i>=0, 3<font face = "symbol">p</font>/4, <font face = "symbol">p</font>, 7<font face = "symbol">p</font>/4
d. <i>x</i>=0, <font face = "symbol">p</font>/4, <font face = "symbol">p</font>, 5<font face = "symbol">p</font>/4
<font size = 4><b>
sin<sup>2</sup><i>x</i> = sin<i>x</i>·cos<i>x</i>

sin<sup>2</sup><i>x</i> - sin<i>x</i>·cos<i>x</i> = 0

sin<i>x</i>(sin<i>x</i> - cos<i>x</i>) = 0

Set each factor = 0

sin<i>x</i> = 0

<i>x</i> = 0, <font face = "symbol">p</font>  that's two solutions

sin<i>x</i> - cos<i>x</i> = 0

sin<i>x</i> = cos<i>x</i>

 sin<i>x</i>
—————— = 1
 cos<i>x</i>

tan<i>x</i> = 1

<i>x</i> = <font face = "symbol">p</font>/4, 5<font face = "symbol">p</font>/4

Solutions: 0, <font face = "symbol">p</font>/4, <font face = "symbol">p</font>, 5<font face = "symbol">p</font>/4, choice d.

Edwin
AnlytcPhil@aol.com</pre>