Prove that cot7(1/2)=√6+√3+√2+2

Steps to prove cot7(1/2)=√6+√3+√2+2

L.H.S

=cot7(1/2)

=cot(15/2)

=(1+sin15)/cos15

={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 cot7(1/2)=√6+√3+√2+2 is proved.

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