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Trignometry

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2 May 2012 07:55:22 IST

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sin and cos

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

If sinA+sinB=1/3 and cosA+cosB=1/4. Then find sin(A+B) and cos(A+B).

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Debal Chakrabarty

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2 May 2012 09:54:35 IST

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sin(A+B)=24/25 and cos(A+B)=7/25).

speed

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2 May 2012 10:11:38 IST

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sin and cos

speed

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2 May 2012 10:14:21 IST

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Can you please tell the steps?

kartikAIR1

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2 May 2012 11:07:16 IST

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(1) sinA+sinB=1/3

=> 2sin((A+B)/2)cos((A-B)/2) = 1/3 ..............(1)

(2) cosA+cosB=1/4

=> 2cos((A+B)/2)cos((A-B)/2) = 1/4 ................(2)

equ(1) / equ(2)

=> tan((A+B)/2) = 4/3

Now use sin(A+B) = 2 tan((A+B)/2)/(1 + tan((A+B)/2)^2)

cos(A+B) = {1- tan((A+B)/2)^2}/{1+ tan((A+B)/2)^2}

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