solve for x

sin^3x+sin^2x+sinx=1

8 Answers

262
Aditya Bhutra ·

can u provide the actual question.

21
Arnab Kundu ·

i think this is the actual question......
solve for x,
for which sin^3x+sin^2x+sinx=1

262
Aditya Bhutra ·

http://www.wolframalpha.com/input/?i=%28sinx%29^3%2B%28sinx%29^2%2Bsinx%3D1
check here- the answer is ridiculous !

21
Arnab Kundu ·

how to solve?

1
chill ·

sin3x+sin2x+sinx=1
(sin2x+1)(sinx+1)=2
0≤ sin2x+1≤2 and 0≤sinx+1≤2
now integral factors of 2 are not possible
therefore
sinx+1=2p and sin2x+1=21-p
where p=[0,1]
hence
x=k(pi)+(-1)karcsin(2p-1) and x=l(pi)±arcsin(21-p-1)
where k,l are integers and p=[0,1]

1
chill ·

i am sorry but this isnt completely correct cause we have a lot of other combinations of prime nos ....anyone else trying?

21
Arnab Kundu ·

hari shankar sir, nishant sir and nasiko sir please try,,,,,,

66
kaymant ·

I think you should check the question once. Though in this case we shall get a single value of sin x, however that is not very pretty and I had to solve the cubic in order to get that value.

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