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Trignometry

Blazing goIITian

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12 Mar 2010 20:11:18 IST

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Prove that: tan70 degrees = 2tan 50 degrees + tan 20 degrees

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Prove that: tan70 degrees = 2tan 50 degrees + tan 20 degrees

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charanjit ghai

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Joined: 23 Nov 2009

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12 Mar 2010 20:29:34 IST

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tan(70-20)=tan50

tan70-tan20/1+tan20 tan70=tan50

tan20 tan70=cot70 tan70=1

tan70-tan20/2=tan50

tan70-tan20=2tan50

tan70=tan20+2tan50

Salonii Sharma

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12 Mar 2010 20:37:21 IST

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Oh yess!! I I'm so dumb. Thanks. :)

edison

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Posts: 7452

31 Jan 2011 21:27:53 IST

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Using

tan(x-y) = [tan(x)-tan(y)]/[1+tan(x)tan(y)],

tan 50 = tan(70 - 20) = [tan(70)-tan(20)]/[1+tan(70)tan(20)]

[tan(70)-tan(20)]/[1+tan(70)tan(20)]=tan50

or [tan(70)-tan(20)]/[1+tan(70)cot(70)]=tan50 {As tan 20 = cot 70)

or [tan(70)-tan(20)]/[1 + 1]=tan50 {As tan70.cot 70 = 1}

or [tan(70)-tan(20)]/2 = tan50

or [tan(70)-tan(20)] = 2 tan50

or tan(70) = 2 tan (50) + tan (20)

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