document.write( "Question 1020475: If sec(θ) = x/2 for 0 < θ < π/2 ,find an expression for ln|sec(θ) + tan(θ)| in terms of x. \n" ); document.write( "

Algebra.Com's Answer #636463 by robertb(5830) $\"\"$ $\"About$

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Note first that $\"theta\"$ is an angle with its terminal side on the 1st quadrant, and so all its trig functions are positive.\r
\n" ); document.write( "\n" ); document.write( "Using the identity $\"sec%5E2%28theta%29+=+1%2Btan%5E2%28theta%29\"$ , we get\r
\n" ); document.write( "\n" ); document.write( " $\"tan%5E2%28theta%29+=+%28x%5E2+-+4%29%2F4\"$ , or $\"tan%28theta%29+=+sqrt%28x%5E2+-+4%29%2F2\"$ , where we chose the positive square root because $\"theta\"$ is in quadrant 1.\r
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\n" ); document.write( "The absolute value bars are not necessary because tangent and secant are positive in quadrant 1. \n" ); document.write( "

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