Posted by **Piwokazi** on Monday, September 12, 2011 at 4:08pm.

Help find the general solution to:sin^2x-3cosx+sinxcosx-3sinx=0

- trig -
**Reiny**, Monday, September 12, 2011 at 6:36pm
sin^2x-3cosx+sinxcosx-3sinx=0

sin^2x - 3sinx + sinxcosx - 3cosx = 0

sinx(sinx - 3) + cosx(sinx - 3) = 0

(sinx - 3)(sinx + cosx) = 0

sinx = 3 , which is not possible

or

sinx = -cosx

sinx/cosx = -1

tanx = -1

x = 135° or 225° or in radians, 3π/4 , 5π/4

the period of tanx = 180° or π radians

general solution: = 3π/4 + kπ

or

x = 5π/4 + kπ , where k is an integer

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