Question

23.
If cos²x+ sin x +1 = 0, and 0<x<2t .
Then x =....?​

Answer 1

Answer:

Given cos²x+sinx+1=0

Now cos²x+sin²x+sinx+1=sin²x

(By adding sin²x both sides)

Then 1+sinx+1=sin²x

or 2+sinx=sin²x

or sin²x-sinx-2=0

or sin²x-2sinx+sinx-2=0

or sinx(sinx-2)+1(sinx-2)=0

or (sinx+1)(sinx-2)=0

or sinx=(-1) or sinx=2

sinx=2 is impossible

So we can take sinx=(-1)

Hence x=270

Hope it helps you

If my answer satisfy anyone then plz give me thanks.

Answer 2

cos^2x + sinx + 1 = 0

sin^2 - sinx - 2 = 0

sinx = 2 or -1/2

by treating it as quadratic eq

sinx=2 is not possible

therefore sinx = -1/2

x= -π/6