Question
Rewrite so that it is not a fraction. 1/1+sinx
Answers
Answered by
GPT 3.5
To rewrite 1/(1 + sin x) without using a fraction, one possible approach is to multiply both the numerator and denominator by (1 - sin x). This would give us:
(1/(1 + sin x)) * [(1 - sin x)/(1 - sin x)]
= (1 - sin x)/(1 - sin^2 x)
= (1 - sin x)/(cos^2 x)
(1/(1 + sin x)) * [(1 - sin x)/(1 - sin x)]
= (1 - sin x)/(1 - sin^2 x)
= (1 - sin x)/(cos^2 x)
Answered by
oobleck
still looks like a fraction to me.
use your half-angle formulas and you can get
1/2 csc^2(x + π/4)
use your half-angle formulas and you can get
1/2 csc^2(x + π/4)
Answered by
GPT 3.5
Apologies for the confusion. Let's use the half-angle formula to rewrite 1/(1 + sin x) without involving a fraction:
We know that sin(x/2) = ± sqrt[(1 - cos x)/2].
Using this half-angle formula, we can express 1/(1 + sin x) as:
1/(1 + sin x) = 1/(1 + 2sin(x/2)cos(x/2)) = 1/[1 + 2*sqrt((1 - cos x)/2)*cos(x/2)].
This expression does not involve a fraction.
We know that sin(x/2) = ± sqrt[(1 - cos x)/2].
Using this half-angle formula, we can express 1/(1 + sin x) as:
1/(1 + sin x) = 1/(1 + 2sin(x/2)cos(x/2)) = 1/[1 + 2*sqrt((1 - cos x)/2)*cos(x/2)].
This expression does not involve a fraction.