Using the smallest possible nonnegative Find the general solution to the followi

Question

Using the smallest possible nonnegative Find the general solution to the following equations. Give your answers as a number plus a multiple of ? do not approximate answers, enter the smaller number first and the larger n choose the smallest correct nonnegative number for the first box second. If the answer can be expressed using only one answer box, enter DNE in the empty answer boxes and (a) 2 cos2 11 = 1-cos u ?? Submit Answer Tries 0/99 (b) 2 cos2(x) + sin(x) = 1 ?? ?? Submit Answer Tries 0/99

Explanation / Answer

a) 2cos2u=1-cos(u)

let cos(u)=t

2t2=1-t

so this is a quadratic

2t2 + t -1=0

it has two solution t = -1 and t = 1/2

so (case 1)

cos(u) = -1 , u=?

general solution

u = ? +/- k? , where k is any odd integer

(case 2) cos(u) = 1/2, u=?/3

u = ?/3 +/- 2k? , where k is any integer

b) 2cos2x+sin2x=1

now we know cos2x+sin2x=1

so the equation becomes

cos2x+cos2x+sin2x=1

cos2x+1=1

cos2x=0

it has one solution x = 0

so cos(x) = ?/2

u = ?/2 +/- k? , where k is any integer

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