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Answer 1 · 2017-01-29T15:18:42

1)
#cos75^@#
#=cos(45+30)#

#=cos45cos30-sin45sin30#

#=1/sqrt2xxsqrt3/2-1/sqrt2xx1/2#
#=(sqrt3-1)/(2sqrt2)#

2)
#sin75^@#
#=sin(45+30)#

#=sin45cos30+cos45sin30#

#=1/sqrt2xxsqrt3/2+1/sqrt2xx1/2#
#=(sqrt3+1)/(2sqrt2)#

3)
#sin((17pi)/6)cos((8pi)/3)-cos((17pi)/6)sin((8pi)/3)#

#=sin((17pi)/6-(8pi)/3)#

#=sin((17pi)/6-(16pi)/6)#

#=sin(pi/6)=1/2#

4)

#cos((7pi)/5))cos((3pi)/5)-sin((7pi)/5))sin((3pi)/5)#

#=cos((7pi+3pi)/5)#

#=cos(2pi)=cos0=1#

5)

#(tan56-tan26)/(1+tan56tan26)#
#=tan(56-26)=tan30=1/sqrt3#

6)

#(tanpi/12+tanpi/6)/(1-tanpi/12tanpi/6)#

#=tan(pi/12+pi/6)#

#=tan((pi+2pi)/12)#

#=tan(pi/4)=1#