document.write( "Question 608023: Hi, I hope someone helps me with this trigonometric equations problem.\r
\n" ); document.write( "\n" ); document.write( "How do you get the solution set of cos^2 2x + 3sin2x = 3 ?\r
\n" ); document.write( "\n" ); document.write( "Also please include the steps. I don't understand our lesson well, especially the part where the reference angle enters. I don't get it at all. Thank yoy for your help! \n" ); document.write( "

Algebra.Com's Answer #383022 by htmentor(1343) $\"\"$ $\"About$

You can put this solution on YOUR website!
cos^2 2x + 3sin2x = 3
\n" ); document.write( "First, we can use the identity cos^2(2x) = 1 - sin^2(2x) to obtain a quadratic in sin(2x):
\n" ); document.write( "1 - sin^2(2x) + 3sin(2x) - 3 = 0
\n" ); document.write( "sin^2(2x) - 3sin(2x) + 2 = 0
\n" ); document.write( "This can be factored as:
\n" ); document.write( "(sin(2x) - 1)(sin(2x) - 2) = 0
\n" ); document.write( "The LHS will be equal to 0 if either sin(2x) = 1, or sin(2x) = 2
\n" ); document.write( "Since the sine of any angle can never be >1, the only solutions are obtained for sin(2x) = 1
\n" ); document.write( "In the 1st quadrant, this gives 2x = 90 deg -> x = 45 deg [ $\"pi\"$ /4]
\n" ); document.write( " \n" ); document.write( "

\n" );