Question

Prove that : cos 20' cos 40' cos 60' cos 80'=1/6​

Answer 1

Answer:

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Step-by-step explanation:

Step 1: Let's multiply both the numerator and denominator of cos20°cos40°cos 60°cos80° by cos10°: Expression =cos20°cos40°cos60°cos80°cos10°cos10°

Step 2： cos80°=sin10° , so here let’s substitute cos80° with sin10° : Expression =cos20°cos40°cos60°sin10°cos10°cos10°

Step 3： cos60°=12 & sin10°cos10°=12sin20°: Expression = cos20°cos40°sin20°2×2cos10°

Step 4： sin20°cos20°=12sin40°: Expression = cos40°sin40°2×2×2cos10°

Step 5： sin40°cos40°=12sin80°: Expression = sin80°2×2×2×2cos10°

Step 6： sin80°=cos10° , we can cancel both factors in the fraction: Expression = 12×2×2×2=116