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Prove that tan20°tan40°tan80°=tan60° |
Answer» tan 40 * tan 80* tan 20=(sin 40 *sin 80) * sin 20 /(cos 40 *cos 80 ) cos 20\xa0now, multiplying numerator and denominator by 2, =(2*sin 40*sin 80) *sin 20 /(2 cos 40*cos 80) cos 20] =(cos 40- cos 120)*sin 20/( (cos 120+ cos 40) cos 20 =(2 cos 40 +1) sin 20 /(2 cos 40-1) cos 20 =(2 cos 40*sin 20 +sin 20) /(2 cos 40 cos 20 -cos 20) =(sin 60 -sin 20 +sin 20)/ (cos 60+sin 20-sin 20) = sin 60/cos 60 =tan 60. |
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