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Trignometry

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 Joined: 4 Mar 2012 Post: 1
4 Mar 2012 13:48:28 IST
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cot(A+15)-tan(A-15)=4cos(2x)/(1+2sin(2A))
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Trigonometry

cot(A+15)-tan(A-15)=4cos(2x)/(1+2sin(2A))

Scorching goIITian

Joined: 20 Jul 2011
Posts: 256
4 Mar 2012 14:59:57 IST
1 people liked this

First of all, the question is cot(A+15)-tan(A-15) = 4cos2A / 1+2sin2A ( You have posted x instead of A)

Now taking L.H.S

cot(A+15) - tan(A-15)

cos(A+15) / sin(A+15)   -   sin(A-15) / cos(A - 15)

[cos(A+15)cos(A-15) - sin(A-15)sin(A+15)] / [ sin(A+15)cos(A-15)

cos2A / sin(A+15)cos(A-15)

2cos2A / 2sin(A+15)cos(A-15)

2cos2A / [sin2A +sin30]

2cos2A / [ sin2A + 1/2]

2cos2A / [(2sin2A+1)/2]

4cos2A / (2sin2A + 1)

= R.H.S

Hence proved....

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