Prove that tan37(1/2)=√6+√3-√2-2

Steps to prove tan37(1/2)=√6+√3-√2-2

L.H.S

=tan37(1/2)

=tan(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 tan37(1/2)=√6+√3-√2-2 is proved.

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