1cos(𝛽)csc(−𝛽)

The given expression is 1cos(𝛽)csc(−𝛽).

Step 1: Understand the trigonometric functions involved. Cos(𝛽) is the cosine of 𝛽 and csc(−𝛽) is the cosecant of -𝛽.

Step 2: Remember that csc(𝛽) = 1/sin(𝛽). Therefore, csc(−𝛽) = 1/sin(−𝛽).

Step 3: Substitute csc(−𝛽) in the expression. We get 1cos(𝛽) * 1/sin(−𝛽).

Step 4: Remember that sin(-𝛽) = -sin(𝛽). Therefore, the expression becomes 1cos(𝛽) * 1/(-sin(𝛽)).

Step 5: Simplify the expression. We get -cos(𝛽)/sin(𝛽).

Step 6: Remember that cos(𝛽)/sin(𝛽) = cot(𝛽). Therefore, the expression simplifies to -cot(𝛽).

So, 1cos(𝛽)csc(−𝛽) simplifies to -cot(𝛽).