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Prove that tan20°tan40°tan80°=tan60°

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Prove that tan20°tan40°tan80°=tan60°

    • Posted by ?Rahul? ?Gusain? 5 years, 2 months ago

    CBSE > Class 11 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 2 months ago

    <pre> tan 40 * tan 80* tan 20=(sin 40 *sin 80) * sin 20 /(cos 40 *cos 80 ) cos 20</pre>

     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.

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