Prove that tan20°tan40°tan80°=tan60°
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Posted by ?Rahul? ?Gusain? 6 years, 10 months ago
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Gaurav Seth 6 years, 10 months ago
now, 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.
2Thank You