Find csc x if sin x + cot x cos x = √3.

Solution:

Given:

sin x + cot x cos x = √3

sin x + (cos x/sin x)cos x = √3.

sin x + cos²x/sinx = √3

(sin²x + cos²x) / sin x = √3

From trigonometric identity:

sin²x + cos²x = 1, hence

1/sin x = √3

cosec x = √3

Find csc x if sin x + cot x cos x = √3.

Summary:

csc x = √3 if sin x + cot x cos x = √3