The value of $\frac{cos8°cos24°cos60°cos66°cos82°}{sin82°sin66°sin60°sin8°sin24°}$ is :
Answer & explanation
Correct answer: option 3
$\frac{cos8°cos24°cos60°cos66°cos82°}{sin82°sin66°sin60°sin8°sin24°}$
Using ,
cos θ = sin ( 90º - θ)
= $\frac{cos(90°-82°)cos(90°-66°)cos60°cos(90°-24°)°cos(90°-8°)}{sin82°sin66°sin60°sin8°sin24°}$
= $\frac{sin8°sin24°cos60°sin66°sin82°}{sin82°sin66°sin60°sin8°sin24°}$
= $\frac{cos60°}{sin60°}$
= cot60°
= \(\frac{1}{√3}\)