If \(tan 35° \cdot tan 55° = \sin θ\), then the smallest positive value of \(θ\) will be ——.

Q.If \(tan 35° \cdot tan 55° = \sin θ\), then the smallest positive value of \(θ\) will be ——.

If \(tan 35° \cdot tan 55° = \sin θ\), then the smallest positive value of \(θ\) will be \(90^\circ\).

\(tan 35° \cdot tan 55° = \sin θ\) Or, \(tan 35° \cdot tan(90° - 35°) = \sin θ\) Or, \(tan 35° \cdot cot 35° = \sin θ\) Or, \(\sin θ = 1\) Or, \(\sin θ = \sin 90°\) \(\therefore θ = 90°\)