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document.write( "Find the exact value of the expression.
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document.write( "tan(sin^−1(2/3)−cos^−1(1/3))
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document.write( "
.\r\n" );
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document.write( "When solving problems like this, half of the success is to reformulate it reasonably.\r\n" );
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document.write( "So I will do it now. We need to calculate 
, where 
= 
and 
= 
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document.write( "So we have the angle in Q1 with 
= 
, and the angle in Q1 with 
= 
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document.write( "Since = 
, the plan is to calculate 
and 
. //Making a good plan is the second half of the success. \r\n" );
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document.write( "To calculate and , we will use well known formulas of Trigonometry\r\n" );
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document.write( " = 
and = 
. (1)\r\n" );
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document.write( " (Regarding these formulas, see the lesson Addition and subtraction formulas in this site). \r\n" );
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document.write( "Looking into the formulas (1), you see that we need to know/to have the values 
and 
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document.write( "in addition to the given values of and . It is easy. \r\n" );
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document.write( "First, = 
= 
= 
= 
. Second, = 
= 
= 
= 
= 
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document.write( "Notice that the signs at square roots are chosen \"+\" since the angles and both lie in Q1.\r\n" );
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document.write( "Now you have everything to calculate and according to (1). //Implementing the plan accurately is the third half of the success.\r\n" );
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document.write( " = 
= 
= 
. (by the way, it shows that 
lies in Q4).\r\n" );
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document.write( " = 
= 
. \r\n" );
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document.write( "And finally 
= 
. (2)\r\n" );
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document.write( "If you rationalize the denominator in (2), you will get the answer = 
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document.write( "Answer. .\r\n" );
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
