Question

solve:cot^2x+3/sinx+3=0

Answer 1

I hope it will help you....

Answer 2

Answer:

Concept: using the formulae of the cotx and sinx

Given:$cot^{2}x +\frac{3}{sinx} +3=0$

To find:  solve the question.

Step-by-step explanation:

In chapter trigonometry there are many types of formulae  from which only following formulae  are used in the question which are

$cotx=secx-1$

and $\frac{1}{sinx} =secx$

so, $cot^{2}x +\frac{3}{sinx} +3=0$

or, $sec^{2}x-1+3secx+3=0$

or, $sec^{2}x-1+3+3secx=0$

or, $secx(secx+1)+2(1+secx)=0$         [∵ rationalization method is used]

or, $(secx+1)(secx+2)=0$

or, $secx=-1$ and $secx=-2$

or, $sinx=-1$  and $sinx=-\frac{1}{2}$

or,  $x=n\pi +(-1)\frac{n\pi }{2}$   or $x=n\pi +(-1)\frac{n\pi }{6}$

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