Use trigonometric identities to simplify the expression.1cos(β)csc(−β)
Question
Use trigonometric identities to simplify the expression.1cos(β)csc(−β)
Solution
The given expression is 1cos(β)csc(−β).
Step 1: We know that csc(−β) = -csc(β) because cosecant is an odd function.
So, the expression becomes 1cos(β)(-csc(β)).
Step 2: We also know that csc(β) = 1/sin(β).
So, the expression becomes 1cos(β)(-1/sin(β)).
Step 3: Simplify the expression to get -cos(β)/sin(β).
Step 4: We know that cos(β)/sin(β) = cot(β).
So, the final simplified expression is -cot(β).
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