document.write( "Question 1046263: what is the minimum value of sin^2(x)+cos^2(x)+sec^2(x)+cosec^2(x)+tan^2(x)+cot^2(x) \n" ); document.write( "
Algebra.Com's Answer #661790 by Alan3354(69443)\"\" \"About 
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sin^2(x)+cos^2(x)+sec^2(x)+cosec^2(x)+tan^2(x)+cot^2(x)
\n" ); document.write( "sin^2 + cos^2 = 1
\n" ); document.write( "= 1 +sec^2(x)+cosec^2(x)+tan^2(x)+cot^2(x)
\n" ); document.write( "sec^2 = tan^2 + 1
\n" ); document.write( "= 1 + tan^2(x) + 1 +cosec^2(x)+tan^2(x)+cot^2(x)
\n" ); document.write( "= 2 + 2tan^2(x) + cosec^2(x) + cot^2(x)
\n" ); document.write( "csc^2 = cot^2 + 1
\n" ); document.write( "= 2 + 2tan^2(x) + cot^2(x)+1 + cot^2(x)
\n" ); document.write( "f(x) = 3 + 2tan^2(x) + 2cot^2(x)
\n" ); document.write( "f'(x) = 4tan*sec^2 - 4cot*csc^2
\n" ); document.write( "tan*sec^2 - cot*csc^2 = 0
\n" ); document.write( "------
\n" ); document.write( "sin/cos^3 - cos/sin^3 = 0
\n" ); document.write( "Muliply thru by sin^3*cos^3
\n" ); document.write( "sin^4 - cos^4 = 0
\n" ); document.write( "(sin - cos)*(sin + cos)*(sin^2 + cos^2) = 0
\n" ); document.write( "sin = cos --> x = pi/4 (principal solution)
\n" ); document.write( "-----
\n" ); document.write( "sin = -cos --> x = 3pi/4 (principal solution)
\n" ); document.write( "-----
\n" ); document.write( "sin^2 = -cos^2 --> no real solution\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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