How to prove the following trignometric identity? \(\displaystyle{\cot{{7}}}{\frac{{{1}}}{{{2}}}}^{\circ}=\sqrt{{{2}}}+\sqrt{{{3}}}+\sqrt{{{4}}}+\sqrt{{{6}}}\)

Aliana Alvarez

Aliana Alvarez

Answered question

2022-04-08

How to prove the following trignometric identity?
cot712=2+3+4+6

Answer & Explanation

xcentricccrhb1

xcentricccrhb1

Beginner2022-04-09Added 12 answers

Alternatively:
cot(7.5)=cos(7.5)sin(7.5)
=2cos2(7.5)sin(15)
=1+cos(15)sin(15)
=2(cos(15)+cos2(15))sin(30)
=4(cos(4530)+1+cos(30)2)
=4(2232+2212+12+34)
=6+2+4+3

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