Find the exact value of the trigonometric expression without

Find the exact value of the trigonometric expression without we use of calculator. Tan (11pi/6 - 3pi/4). Tan (11pi/6 - 3pi/4) =

tan( 11pi/6 -3pi/4)

= {tan(11pi/6) - tan(3pi/4) }/( 1 + tan11pi/6*tan3pi/4)

tan( 11pi/6) = -tanpi/6 = -1/sqrt3

tan(3pi/4) = tan(pi -pi/4) = -1/sqrt2

tan( 11pi/6 -3pi/4)

= {tan(11pi/6) - tan(3pi/4) }/( 1 + tan11pi/6*tan3pi/4)

={ -1/sqrt3 +1/sqrt2 }/( 1+1/sqrt6)

= ( sqrt3 - sqrt2)/(sqrt6 +1)

Rationalise the denominator:

=(sqrt3 - sqrt2)(1- sqrt6)/(-5)

= -(sqrt3 - sqrt18 -sqrt2 +sqrt12)/5

= -(sqrt3 -3sqrt3 -sqrt2 +2sqrt3)/5

= -(-sqrt2)/5

= sqrt2/5