The expression (1 − cos²θ)(1 + cot²θ) simplifies to:

1. 1 − cos²θ = sin²θ and 1 + cot²θ = cosec²θ = 1/sin²θ. Their product is sin²θ × 1/sin²θ = 1.

The expression (1 − co $s^{2}$ θ)(1 + co $t^{2}$ θ) simplifies to:

Competition practiceTrigonometry

1 − co

s^{2}

θ = si

n^{2}

θ and 1 + co

t^{2}

θ = cose

c^{2}

θ = 1/si

n^{2}

θ. Their product is si

n^{2}

θ × 1/si

n^{2}

θ = 1.

Answer: A) 1

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