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Prove that Tan20 tan30 tan40 tan80 …

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Prove that Tan20 tan30 tan40 tan80 =1

Posted by Shariq Ahmad 8 years, 3 months ago

CBSE > Class 11 > Mathematics

2 answers

Gaurav Seth 5 years, 4 months ago

Step -by -step explanation: tan20° tan40° tan80° = 2sin20°sin40°sin80°/2cos20°cos40°cos80° = {cos(20°-40°)-cos(20°+40°)}sin80°/{cos(20°+40°)+cos(20°-40°)}cos80° = (cos20°-cos60°)sin80°/(cos60°+cos20°)cos80° = {2cos20°sin80°-2(1/2)sin80°}/{2(1/2)cos80°+2cos20°cos80°} [∵,cos60°=1/2] = {sin(20°+80°)-sin(20°-80°)-sin80°}/{cos80°+cos(20°+80°)+cos(20°-80°)} = (sin100°+sin60°-sin80°)/(cos80°+cos100°+cos60°) = {2cos(100°+80°)/2sin(100°-80°)/2 +√3/2}/{2cos(100°+80°)/2cos(100°-80°)/2+1/2} [∵, sin60°=√3/2 and cos60°=1/2] = (2cos90°sin10°+√3/2)/(2cos90°cos10°+1/2) = (√3/2)/(1/2) [∵, cos90°=0] = √3 = tan60° Now, tan30°tan60° = *= 1

Utkarsh Raj 8 years, 3 months ago

Convert it into sin and cos

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