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i get x = 225 or 315 when 0 <= x <= 360 degrees.
\n" ); document.write( "if your domain is not restricted, then the answer would be:
\n" ); document.write( "x = 225 +/- 360*n and x = 315 +/- 360*n
\n" ); document.write( "this is because the sin is negative in the third and fourth quadrant.
\n" ); document.write( "i solved as follows:
\n" ); document.write( "sqrt(2)*sec(x) + 2*tan(x) = 0
\n" ); document.write( "since sec(x) is equal to 1/cos(x) and tan(x) is equal to sin(x)/cos(x), the equation becomes:
\n" ); document.write( "sqrt(2)/cos(x) + 2*sin(x)/cos(x) = 0
\n" ); document.write( "since the denominator is the same, you can combine the 2 terms to get:
\n" ); document.write( "(sqrt(2) + 2*sin(x)) / cos(x) = 0
\n" ); document.write( "multiply both sides of the equation by cos(x) to get:
\n" ); document.write( "sqrt(2) + 2*sin(x) = 0
\n" ); document.write( "subtract sqrt(2) from both sides of the equation to get:
\n" ); document.write( "2*sin(x) = -sqrt(2)
\n" ); document.write( "divide both sides of the equation by 2 to get:
\n" ); document.write( "sin(x) = -sqrt(2)/2
\n" ); document.write( "since sin(45) = sqrt(2)/2 and sine is negative in the third and fourth quadrant, then the angle must be 225 degrees (third quadrant) or 315 degrees (fourth quadrant).
\n" ); document.write( "since the sine and cosine functions are repetitive every 360 degrees, then you'll get the same sine every multiple of 360 degrees.
\n" ); document.write( " \n" ); document.write( "