Prove that cot37(1/2)=√6-√3-√2+2

Steps to prove cot37(1/2)=√6-√3-√2+2

L.H.S

=cot37(1/2)

=cot(75/2)

=(1+cos75)/sin75

={1+(√3-1/2√2)}/(√3+1/2√2)

=(2√2+√3-1)/(√3+1)

=(2√2+√3-1)(√3-1)/(√3+1)(√3-1)

=(2√6-2√3-2√2+4)/3-1

=(2√6-2√3-2√2+4)/2

=2(√6-√3-√2+2)/2

=√6-√3-√2+2

=R.H.S

Hence cot37(1/2)=√6-√3-√2+2 is proved. 

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