Prove tan &#x2061;<!-- ⁡ --> 84 <mrow class="MJX-TeXAtom-ORD"> &#x2218;<

Axel York

Axel York

Answered question

2022-06-03

Prove tan 84 = tan 78 + tan 72 + tan 60

Answer & Explanation

Siffkiffanewsler6n

Siffkiffanewsler6n

Beginner2022-06-04Added 7 answers

Note that
cos 36 cos 72 = 2 cos 36 cos 72 = sin 72 cos 72 sin 36 = sin 144 2 sin 36 = 1 2
Thus
tan 78 + tan 72 + tan 60 = 1 2 cos 72 cos 78 + cot 30 = 2 cos 36 cos 78 + 2 cos 30 = 2 cos 36 + 2 cos 30 cos 78 cos 78 = 2 cos 36 cos 72 + cos 48 sin 12 = 1 + cos 72 + cos 48 sin 12 = 1 + cos 12 sin 12 = 2 cos 2 6 2 sin 6 cos 6 = tan 84

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?