Example 12 - Find value of tan 13pi/12 - Chapter 3 Class 11 - (x + y) formula

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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E ample, 12 Find the value of tan 13 /12 tan 13 /12 Putting = 180 = tan ( (13 180 )/12 ) = tan (13 15 ) = tan (195 ) = sin 195 / 195 = (180 + 15 ) / (180 + 15 ) We know that sin (180 + ) = sin & cos (180 + ) = cos = sin 15 / cos 15 = 15 / 15 = tan 15 = tan (45 30 ) Using tan (x - y) = ( )/(1+ ) Here putting x = 45 and y = 30 = (tan 45" " tan 30" " )/(1 + tan 45" " tan 30" " ) = (1 1/ 3)/(1 + 1 1/ 3) = (( 3 1" " )/ 3)/(( 3 + 1" " )/ 3) = ( 3 1)/ 3 3/( 3 + 1) = ( 3 1)/( 3 + 1) Rationalizing the same = ( 3 1)/( 3 + 1) ( 3 1)/( 3 1) = ( 3 1)2/( 3 + 1)( 3 1) Using (a b )2 = a2 + b2 2ab = (( 3)2 +(1)2 2" " 3 1)/( 3 + 1)( 3 1) = (3 + 1 2 3)/( (3 )+ 1)( 3 1) Using (a b ) (a + b) = a2 b2 = (4 2 3)/(( 3)2 (1)2) = (4 2 3)/(3 1) = (4 2 3)/2 = (2 (2 (3 )))/2 = 2 3 Hence tan 13 /12 = 2 3

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