2. Solve the following equations for 0° Sx < 180°.

(i) cosec (x+10°) = 3

(ii) cot (x - 30°) = 0.45.

See below in bold.

Step-by-step explanation:

(1) cosec (x + 10) = 3

Now cosec x = 1/sin x so

1 / sin (x + 10) = 3

3 sin (x + 10) = 1

sin (x + 10) = 1/3

x + 10 = 19.47, 160.53 degrees

x = 9.47, 150.53 degrees.

(ii) cot (x - 30) = 0.45

cot (x - 30) = 1 / tan (x - 30) so we have

tan (x - 30) = 1 / 0.45 = 2.2222

x - 30 = 65.77 degrees

x = 95.77 degrees.