Question
Download Solution PDFWhat will be the value of \(\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}\)
Concept used:
Sin α = Cos (90° - α)
Calculation:
\(\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}\)
⇒ \(\frac{\cos (90 - 30)^{\circ} \cos (90 - 40)^{\circ} \cos (90 - 50)^{\circ} \cos (90 - 60)^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}\)
⇒ \(\frac{\cos 60^{\circ} \cos 50^{\circ} \cos 40^{\circ} \cos 30^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}\)
⇒ 1
∴ The required value is 1.
Last updated on Jul 17, 2025
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