Question #7318f

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Answer 1 · 2016-07-14T07:41:29

The question has not been written properly.

Given
#cscx=3," where " 90^@ < x < 180^@#

So #45^@ < x/2 < 90^@#

#=>sinx=1/3#

#90^@ < x < 180^@->cosx" is negative"#

#:.cosx=-sqrt(1-sin^2x)=-sqrt(1-1/9)#
#=-(2sqrt2)/3#

#"Now "cos(x/2)=sqrt(1/2(1+cosx))#

#=sqrt(1/2(1-(2sqrt2)/3))#

#=sqrt(1/6(3-2sqrt2))#

#=sqrt(1/6((sqrt2)^2+1^2-2sqrt2*1)#

#=sqrt(1/6(sqrt2-1)^2#

#=1/sqrt6(sqrt2-1)#

#"Again "sin(x/2)=sqrt(1/2(1-cosx))#

#=sqrt(1/2(1+(2sqrt2)/3))#

#=sqrt(1/6(3+2sqrt2)#

#=sqrt(1/6((sqrt2)^2+1^2+2sqrt2*1)#

#=sqrt(1/6(sqrt2+1)^2#

#=1/sqrt6(sqrt2+1)#

#:.tan(x/2)=(sin(x/2))/(cos(x/2))=(sqrt2+1)/(sqrt2-1)#

# =(sqrt2+1)/(sqrt2-1)*(sqrt2+1)/(sqrt2+1)#

#=(sqrt2+1)^2/(2-1)=3+2sqrt2#