document.write( "Question 31257: tan theta + cot theta = 1 over the sin theta times cos theta
\n" ); document.write( "It asks me to:
\n" ); document.write( "\"Verify the Identity. Justify each step.\" \n" ); document.write( "

Algebra.Com's Answer #168826 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
(Since Algebra.com's formula software does not \"do\" theta for some reason, I'll use x, instead).

\n" ); document.write( "As a general rule, when you are trying to solve a Trig. problem and you don't see any better way, express everything in terms of sin and cos. This will usually result in something you can figure out.

\n" ); document.write( "Using this on your expression:
\n" ); document.write( " $\"tan%28x%29+%2B+cot%28x%29+=+1%2F%28sin%28x%29%2Acos%28x%29%29\"$
\n" ); document.write( "Replacing tan(x) with sin(x)/cos(x) and cot(x) with cos(x)/sin(x):
\n" ); document.write( " $\"sin%28x%29%2Fcos%28x%29+%2B+cos%28x%29%2Fsin%28x%29+=+1%2F%28sin%28x%29%2Acos%28x%29%29\"$
\n" ); document.write( "Verifying identities often involves changing the equation, using proper Trig. and/or Algebra, so that the two sides match. So we will try to match the left and right sides. Since the right side is a single fraction, we'll go ahead and add the two fractions on the left tomake the left side one fraction. And to add fractions we nedd, of course, the same denominator:
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\n" ); document.write( "Adding we get:
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\n" ); document.write( "Since the numerator is part of a well known Trig. identity: $\"%28sin%28x%29%29%5E2+%2B+%28cos%28x%29%29%5E2+=+1\"$ , we get:
\n" ); document.write( " $\"1%2F%28sin%28x%29%2Acos%28x%29%29+=+1%2F%28sin%28x%29%2Acos%28x%29%29\"$
\n" ); document.write( "And we have matched the left and right sides which verifies the identity!\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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