Use trigonometric identities to simplify the expression.cot(β)cos(β)

Sure, let's simplify the expression cot(β)cos(β) using trigonometric identities.

Step 1: Recall the definition of cotangent. Cotangent is the reciprocal of tangent, so cot(β) = 1/tan(β).

Step 2: Replace cot(β) in the expression with 1/tan(β). So, cot(β)cos(β) becomes (1/tan(β))cos(β).

Step 3: Recall the definition of tangent. Tangent is the ratio of sine to cosine, so tan(β) = sin(β)/cos(β).

Step 4: Replace tan(β) in the expression with sin(β)/cos(β). So, (1/tan(β))cos(β) becomes (1/(sin(β)/cos(β)))cos(β).

Step 5: Simplify the expression. The cos(β) in the numerator and the cos(β) in the denominator cancel out, leaving 1/sin(β).

So, cot(β)cos(β) simplifies to 1/sin(β), or csc(β), the cosecant of β.