Question

hello, can someone help me with this, please: Find all solutions of sin x + cos x - sin x cos x = sin^2x + cos^2x in the interval [0; 2]

Answer 1

do you have some idea where to start?

Answer 2

yep, simplifying, but kinda stuck there

Answer 3

well, on that right side sin^2x+cos^2x equals 1 right

Answer 4

yap

Answer 5

but i dont think that's the right way tho

Answer 6

do you have any idea?

Answer 7

you know i am trying to do some calculus work myself, and i am also trying to think of something for your problem, give me 5 min

Answer 8

sin x + cos x - sin x cos x = sin^2x + cos^2x


sin x + cos x - sin x cos x = 1


sin x + cos x - sin x cos x - 1 = 0


sin x - sin x cos x + cos x- 1 = 0


(sin x - sin x cos x) + (cos x- 1) = 0


-sin x(-1 + cos x) + 1(cos x- 1) = 0


-sin x(cos x -1) + 1(cos x- 1) = 0


(-sin x + 1)(cos x- 1) = 0


-(sin x - 1)(cos x- 1) = 0


(sin x - 1)(cos x- 1) = 0


From here, solve sin x - 1 = 0 and cos x - 1 = 0

Answer 9

thank you so much