Question

solve each equation for 0 less than or equal to x greater than 2ð.

cot²x-cscx=1

thanks:)

step by step please :)

Answer 1

cot²x-cscx=1
Use 1+cot²(x)=csc²(x)
(csc²(x)-1-csc(x)-1=0
csc²(x)-csc(x)-2=0
Let c=csc(x)
c²-c-2=0
Solve for c:
(c-2)(c+1)=0
c=2 or c=-1
=> sin(x)=1/2 or sin(x)=-1
=> x=π/6, 5π/6 or x=3π/2

The solution can be obtained by memorized exact values of sin(x), or you can see plot of sin(x) between 0 to 2π for solution.
http://img846.imageshack.us/i/1299722695.png/