How do you solve #2sinx -1 = cscx#?

1 Answer
Noah G
Jan 12, 2018

#x = 330˚, 210˚, 90˚#

Explanation:

Rewrite in terms of sine.

#2sinx - 1 = 1/sinx#

#sinx(2sinx - 1) = 1#

#2sin^2x - sinx - 1 = 0#

#2sin^2x - 2sinx + sinx - 1 = 0#

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

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

#sinx = -1/2 or sinx = 1#

When #sinx = -1/2# we will be in the 3rd and 4th quadrants. Therefore, #x = 180˚ + 30˚ = 210˚# and #x = 360˚ - 30˚ = 330˚#

When #sinx = 1#, x will equal #90˚#.

Hopefully this helps!

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