document.write( "Question 1081080: If tan x + cot x = 2, then find the value tan^17 x + cot^17 x \n" ); document.write( "

Algebra.Com's Answer #695169 by ikleyn(52864) $\"\"$ $\"About$

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document.write( "If tan(x) + cot(x) = 2, then \r\n" );
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document.write( "    +  = 2,  ---->\r\n" );
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document.write( "    +  = 2,  ---->\r\n" );
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document.write( "    = 2,  ---->\r\n" );
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document.write( "    = 2,\r\n" );
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document.write( "   2sin(x)*cos(x) = 1  --->  sin(2x) = 1  --->  2x =   --->  x =   or  x = . \r\n" );
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document.write( "   In any case, tan(x) = 1  and  cot(x) = 1.\r\n" );
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document.write( "       So, we proved that  if  tan(x) + cot(x) = 2  then  tan(x) = 1  and  cot(x) = 1.\r\n" );
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document.write( "2.  Having this, you have   =  = 1 + 1 = 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. if tan(x) + cot(x) = 2 then $\"tan%5E17%28x%29+%2B+cot%5E17%28x%29\"$ = 2.\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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