Question

if cot²x+cosec x -a = 0 has one solution then what is the value of a​

Answer 1

Step-by-step explanation:

I think u r asking find the value of x...

Answer 2

complete Question:

If cot²x+cosec x -a = 0 has one solution then what is the value of x ?

Answer:

The value of x is  

${cosec}^{ - 1} (\frac{ - 1±i \sqrt{3 + 4a} }{2} )$

Step-by-step explanation:

Cot²x+Cosec x -a = 0

→(Cosec²x − 1) + Cosecx − a = 0

(Cosec²x) + Cosecx − (a + 1) = 0

Now using Formula-

$x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a}$

Hence,

$\csc(x) = \frac{ - 1± \sqrt{ {1}^{2} - 4(a + 1) } }{2 \times 1}$

$= \frac{ - 1± \sqrt{ - (3 + 4a)} }{2} = \frac{ - 1±i \sqrt{3 + 4a} }{2}$

$x = {cosec}^{ - 1} (\frac{ - 1±i \sqrt{3 + 4a} }{2} )$

Used formula is

$cosec(p) = q \\ p = {cosec}^{ - 1} (q)$