Question

find the principal solution of Cot x = -1​

Answer 1

Answer:

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Step-by-step explanation:

principal value of cotx is all real no. & x should belongs between (0,180)

cotx= -1

X = 3π/4 or 135

Hence, X belongs between (0,180)

Answer 2

Answer:

$x = \frac{3\pi}{4} + k\ \: \pi \: k \: ez$

Alternate form :- x = k × 180°, k € Z

Step-by-step explanation:

Determine the defined range.

Cot (x) = -1, x ≠ k π, k € Z

To isolate x, use the inverse trigonometric function.

x = arccot (-1)

Use a trigonometric values table or unit circle to find the value of arccot (-1).

$x = \frac{3\pi}{4}$

Since the cot (x) is a periodic, add the period of k π, k € Z, to find all solutions.

$x = \frac{3\pi}{4} + k \: \pi \: k \: e \: z$

Alternate form :-

x = 135° + k × 180°, k € Z