How do you solve #sinx/(1 - sinx) - sinx/(sinx + 1) = 2#?

1 Answer
Noah G
Feb 7, 2018

#x = pi/4 + pi/2n#

Explanation:

We start by putting on a common denominator:

#(sinx(sinx + 1) - sinx(1 - sinx))/((sinx + 1)(1 - sinx)) = 2#

Now we can expand.

#(sin^2x + sinx - sinx + sin^2x)/(sinx - sinx + 1 - sin^2x) = 2#

#(2sin^2x)/(1 - sin^2x) = 2#

#2sin^2x = 2 - 2sin^2x#

#4sin^2x= 2#

#sin^2x= 1/2#

#sinx = +- 1/sqrt(2)#

Use the #pi/4-pi/4-pi/2# triangle:

#x = pi/4 + pi/2n#

Hopefully this helps!

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