# Write the value of sin2 θ cos2 θ (1 + tan2 θ)(1 + cot2 θ).

Consider sin2 θ cos2 θ (1 + tan2 θ)(1 + cot2 θ)

= sin2 θ cos2 θ (sec2 θ)(cosec2 θ) ( 1 + cot2 θ = cosec2 θ and 1 + tan2 θ = sec2 θ)

= sin2 θ (cosec2 θ) cos2 θ (sec2 θ)

= 1 × 1

= 1

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