SOLUTION: 4sinx-2cscx=0

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Question 546250: 4sinx-2cscx=0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
4sin%28x%29-2csc%28x%29=0
csc%28x%29=1%2Fsin%28x%29
so the equation really is
4sin%28x%29-2%2Fsin%28x%29=0
To save some writing, let's change variables for a little while. Let's call it y, y=sinx
The equation can be written as
4y-2%2Fy=0
Multiplying times y
4y%5E2-2=0 <--> 4y%5E2=2
The solutions would be y=sqrt%282%29%2F2 and y=-sqrt%282%29%2F2
You must know that between 0 and 2pi, there are 4 angles that give those values for sin(x):
sin%28pi%2F4%29=sin%283pi%2F4%29=sqrt%282%29%2F2
and sin%285pi%2F4%29=sin%287pi%2F4%29=-sqrt%282%29%2F2
To cover all infinity of solutions x=%282k%2B1%29pi%2F4 with k=any integer.