Question

Find all solutions of the equation algebraically:
csc x + cot x = 1

Answer 1

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Answer 2

30°, 150° and 270°

Answer 3

How did you get that?

Answer 4

csc(x) + cot(x) = 1
1/sin(x) + cos(x)/sin(x) = 1
1 + cos(x) = sin(x)
sin(x) - cos(x) = 1

Square both sides
sin²(x) - 2sin(x)cos(x) + cos²(x) = 1
1 - 2sin(x)cos(x) = 1
sin(2x) = 0

2x = {0, π, 2π, 3π}
x = {0, π/2, π, 3π/2}

Check
csc(0) + cot(0) is undefined
csc(π/2) + cot(π/2) = 1
csc(π) + cot(π) is undefined
csc(3π/2) + cot(3π/2) = -1

The only value of x that satisfies this equation in the interval
[0, 2π) is x=π/2

Answer 5

primary lesson Trigono... :)