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Home / Doubts and Solutions/ICSE/Class 11 Science/Mathematics

Prove it

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Asked by nishabr7 24th August 2020, 10:49 PM
Answered by Expert
Answer:
To perove: tan20 tan40 tan80 = tan 60
tan 20 space tan 40 space tan 80 space equals space fraction numerator sin 20 space sin 40 space sin 80 over denominator cos 20 space cos 40 space cos 80 end fraction equals fraction numerator open parentheses 2 space sin 40 space sin 80 close parentheses space sin 20 over denominator open parentheses 2 space cos 40 space cos 80 close parentheses space cos 20 end fraction equals fraction numerator open parentheses cos 40 minus cos 120 close parentheses space sin 20 over denominator open parentheses cos 40 plus cos 120 close parentheses space cos 20 end fraction equals fraction numerator open parentheses 2 cos 40 plus 1 close parentheses space sin 20 over denominator open parentheses 2 cos 40 minus 1 close parentheses space cos 20 end fraction equals fraction numerator 2 cos 40 space sin 20 space plus space sin 20 over denominator 2 cos 40 space cos 20 space minus space cos 20 end fraction equals fraction numerator sin 60 minus sin 20 plus sin 20 over denominator cos 60 plus sin 20 minus sin 20 end fraction equals fraction numerator sin 60 over denominator cos 60 end fraction equals tan 60
Answered by Expert 25th August 2020, 12:56 PM
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Tags: trigonometric-identities basic-trigonometric-formulae trigonometric-ratios
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