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Trignometry
sudhindra shenoy's Avatar
sudhindra shenoy
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16 Oct 2011 16:07:28 IST
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trigonometric question
Mathematics

 Prove that

cot16 cot44+cot44 cot76-cot76 cot16=3


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hemang's Avatar

hemang
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17 Oct 2011 12:27:31 IST
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cot16*cot44+cot44*cot76-cot76*cot16 = 3

or, tan46*tan74 + tan46*tan14 - tan14*tan74 = 3

or, tan46*tan74 + tan46*tan14 - tan14*tan74 + 1 = 4

or, LHS = tan74(tan46-tan14) + (1+tan46*tan14)

or, tan74(tan32)(1+tan46*tan14) + (1+tan46*tan14)

or, (1+tan46*tan14)(1 + tan32*tan74)

or, cos32*cos42/(cos46*cos14*cos32*cos74)

or, cos42/(cos46*cos14*cos74) .....(1)

now cos(x)*cos(60-x)cos(60+x) = 1/4cos(3x)

put x = 14 to get

cos46*cos14*cos74 = 1/4*cos42 putting this in (1)

we get LHS = 4 = RHS.

hence proved....

like my post if you apprecite it.

 

 

 
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MRITYUNJOY DE
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Joined: 17 Oct 2011
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17 Oct 2011 14:28:29 IST
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trigonometric question
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VISHAL VAIBHAV's Avatar

VISHAL VAIBHAV
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17 Oct 2011 15:36:11 IST
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where to practice tough trigonometric ques. (with solution)
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Ayush Shaw's Avatar

Ayush Shaw
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17 Oct 2011 18:45:14 IST
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Yaar S. Loney book are good

 
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Ayush Shaw's Avatar

Ayush Shaw
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17 Oct 2011 18:45:15 IST
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Yaar S. Loney book are good

 
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hemang's Avatar

hemang
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18 Oct 2011 12:12:08 IST
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S L loney is good.

sorry i wrote "apprecite". it should have been "appreciate"...
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sudhindra shenoy's Avatar

sudhindra shenoy
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19 Oct 2011 06:14:43 IST
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 @ hemang ur answer is good

but i didn't understand from the step    (1+tan46tan14)(1+tan74tan32)
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sudhindra shenoy's Avatar

sudhindra shenoy
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19 Oct 2011 06:15:02 IST
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 plz help
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hemang's Avatar

hemang
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19 Oct 2011 12:02:03 IST
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(1+tan46*tan14)(1 + tan32*tan74)

or, (cos46*cos14 + sin46*sin14)(cos32*cos74 + sin32*sin74)/(cos46*cos14*cos32*cos74)

or, [cos(46-14)*cos(32-74)]/(cos46*cos14*cos32*cos74)

or, [cos32*cos42]/(cos46*cos14*cos32*cos74) = cos42/(cos46*cos14*cos74)

i used this -

1 + tanA*tanB = cos(A-B)/(cosA*cosB).

 
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Manasi's Avatar

Manasi
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Joined: 1 Dec 2006
Posts: 2108
11 Feb 2012 14:42:48 IST
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hemang has solved the question already...thanx :)
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