Solve each trigonometric equation such that 0 ≤ xx ≤ 2?. Give answers in exact form.

a. √2cos (x) + 1 = 0

b. tan (x) - √3 = 0

c. sin2 (x) - 1 = 0

Answer: a) 120° b) 60° c) 45°

Step-by-step explanation:

a) a. √2cos (x) + 1 = 0

We need to make 'x' the subject of the formula first

√2cos (x) = 0-1

√2cos (x) = - 1

Cos (x) = - 1/√2

x = arccos (-1/2)

x = - 60°

Since cosine is negative in second and third quadrant, X = 180-60 = 120° (2nd quadrant)

X = 180+60 = 240° (3rd quadrant)

We will go for x = 120° being the lesser value.

b) tan (x) - √3 = 0

tan (x) = √3

x = arctan√3

x = 60°

c) sin2x-1 = 0

Sin2x = 1

2x = arcsin1

2x = 90°

x = 90°/2

x = 45°