Question

Prove that:-


Tan20° tan 40° tan 80°=tan 60°


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Answer 1

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i will try to help you

taking L.H.S ,

tan 40 * tan 80* tan 20=(sin 40 *sin 80) * sin 20 /(cos 40 *cos 80 ) cos 20

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

=tan60.........proved

Answer 2

Step-by-step explanation:

Lhs=tan20*tan40*tan80

=Sin20*sin80*sin40/cos20* cos80*cos40

=(2sin20*sin80)sin40/(2cos20*cos80)cos40

=(cos60-cos100)sin40/(cos60+cos100)cos40

=½sin40-cos100sin40/½cos40+cos100cos40

=Sin40-2cos100sin40/cos40+2cos100cos40

=Sin40-sin140+sin60/cos40+cos140+cos60

=Sin40-sin(180–40)+sin60/cos40+cos(180–40)+cos60

=Sin40-sin40+sin60/cos40-cos40+cos60

=Sin60/cos60=tan60=Rhs.

Therefore,proved

hope it will helps u