Solve equation 2 cot² x + 2 = 7 + 3 cot x for 0 \leqslant x \leqslant 360 ​

Question

Solve equation 2 cot² x + 2 = 7 + 3 cot x for

`0 \leqslant x \leqslant 360`
​

Answer 1

Look below.

Explanation:

`2 (cotx)^(2) + 2 = 7 + 3 cot x\\let \\ u=cotx\\2u^2+2=7+3u\\2u^2-3u-5=0\\`
`x=(-(-3)+√(9-4(2)(-5))) )/(2(2)) \\x=(-(-3)-√(9-4(2)(-5))) )/(2(2)) \\x={11/4}\\x=-1\\\\u=cotx\\x=arccotu\\x_(1)=arccot(-1) \\x_(2)=arccot(11/4)\\`

Calculate x1 and x2 in calculator. Check for domain.