Math, asked by Sharmaankit, 1 year ago

prove that cotπ/24=√2+√3+√4+√6​

Answers

Answered by janmayjaisolanki78
5
Converting Cot(π/24) into degrees by multiplying the angle by 180/π we can get
Cot(π/24)= cot (15/2)
Now using the formula
cotA= (1+cos2A)/sin2A
We can write
Cot (15/2)= (1+cos15°)/sin15°……………(1)
Now
cos15°= cos (45°-30°)
=cos45.cos30+sin45.sin30
=1/√2.√3/2+1/√2.1/2
=> cos 15°= (1/4) (√6 + √2)
Similarly sin15° = (1/4) (√6 - √2)
Putting these values in eq. (1)
Cot (15/2)= [1 + (1/4) (√6 + √2)] / [(1/4) (√6 - √2)] 
= (4 + √6 + √2) / (√6 - √2)
On rationalisation 
Cot (15/2)= [(4 + √6 + √2) * (√6 + √2)] / [(√6 - √2) * (√6 + √2)] 
= (4√6 + 6 + 2√3 + 4√2 + 2√3 + 2) / 4 
= (4√2 + 4√3 + 8 + 4√6) / 4 
= √2 + √3 + √4 + √6.
=7.596

janmayjaisolanki78: Plz mark as brainliest
Similar questions