a Find all solutions in the interval 0 2 rounded to five dec

(a) Find all solutions in the interval [0, 2), rounded to five decimal places. (Enter your answers as a comma-separated list.)

4 cos 2 = 2

theta=

(b) Find the exact value of

cos(2tan^-1 4/3)

(c)Rewrite the expression as an algebraic function of x and y.

cos(sin¹ x tan¹ y)

4 cos 2 theta = 2

cos 2 theta = 2/4

cos 2 theta = 1/2

theta = ( pi + 6pi*n ) / 6 , (5pi + 6pi*n )/ 6

solutions are

theta = 7pi/6 , 5pi/6 , pi/6 , 11pi/6

b) cos ( 2tan^-1 4/3)

let tan^-1 4/3 = x

tan x = 4/3

cos x = 3/5

sin x = 4/5

cos ( 2tan^-1 4/3) = cos 2 x

applying double angle formula

cos 2x = cos^2 x - sin^2 x = (3/5)^2 - (4/5)^2 = 9/25 - 16/25 = -7/25

cos ( 2tan^-1 4/3) = -7/25