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Given expression: sec(θ)/ cosec(θ)

Now, secant of an angle, sec(θ) can also be written as 1/ cos(θ).

Similarly, cosec of an angle, cosec(θ) can also be written as 1/sin(θ).

Therefore, sec(θ)/ cosec(θ) = (1/cos(θ))/ (1/sin(θ))

Taking the reciprocal, we get: sin(θ)/ cos(θ)

Now we know that,

Given expression: [tan(θ) * cot(θ)]/ [cosec(θ)]

Now we know that tan(θ) = sin(θ)/ cos(θ)

Also,

Substituting this, we get: [tan(θ) * cot(θ)]/ [cosec(θ)] = [tan(θ) * 1/tan(θ)]/ [1/sin(θ)]

Hence this gives: 1/ [1/sin(θ)] = sin(θ) (By taking the reciprocal)