document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210538>Question 1210538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values of x in the range 0°≤x≤360°, which satisfy the equation below\r<BR>\n" );
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document.write( "i) sin3xsinx = 2cos2x + 1\r<BR>\n" );
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document.write( "ii) 3cotx + tanx - 4 = 0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #853497 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=853497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve these trigonometric equations, we will use fundamental identities to simplify them into a solvable form.\r<BR>\n" );
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document.write( "## i) \r<BR>\n" );
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document.write( "To solve this, we can use the **Product-to-Sum formula**:\r<BR>\n" );
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document.write( "**Step 1: Apply the formula to the left side.**<BR>\n" );
document.write( "Let  and :\r<BR>\n" );
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document.write( "**Step 2: Simplify and rearrange.**<BR>\n" );
document.write( "Multiply the entire equation by :\r<BR>\n" );
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document.write( "**Step 3: Use the Double Angle formula for .**<BR>\n" );
document.write( "Recall that . Here, let :\r<BR>\n" );
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document.write( "**Step 4: Factor the quadratic.**<BR>\n" );
document.write( "Let :\r<BR>\n" );
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document.write( "So,  or .\r<BR>\n" );
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document.write( "**Step 5: Solve for  in the range .**<BR>\n" );
document.write( "Since , then .\r<BR>\n" );
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document.write( "* **Case 1: **\r<BR>\n" );
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document.write( "* **Case 2: **\r<BR>\n" );
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document.write( "**Solution (i):** \r<BR>\n" );
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document.write( "## ii) \r<BR>\n" );
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document.write( "**Step 1: Rewrite  in terms of .**<BR>\n" );
document.write( "Since , the equation becomes:\r<BR>\n" );
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document.write( "**Step 2: Form a quadratic equation.**<BR>\n" );
document.write( "Multiply through by  (noting that ):\r<BR>\n" );
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document.write( "**Step 3: Factor the quadratic.**\r<BR>\n" );
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document.write( "So,  or .\r<BR>\n" );
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document.write( "**Step 4: Solve for  in the range .**\r<BR>\n" );
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document.write( "* **Case 1: **\r<BR>\n" );
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document.write( "* **Case 2: **\r<BR>\n" );
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document.write( "**Solution (ii):** \r<BR>\n" );
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document.write( "Would you like me to show you how to verify these solutions using their respective graphs? </SPAN>\n" );
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