trig

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

cot²x-cscx=1

thanks:)

step by step please :)

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  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/

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