Trignometry

Harpreet aka MAX's Avatar
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Joined: 20 Oct 2008
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1 Mar 2009 19:53:04 IST
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cos(A+B) + sin(A-B) = 2sin (45+A)cos(45+B)
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Trigonometry

cos(A+B) + sin(A-B) = 2sin (45+A)cos(45+B)



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Vikram Saxena's Avatar

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Joined: 1 Apr 2007
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2 Mar 2009 00:32:39 IST
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 apply the formula of :

2 sin A . cos B in RHS.......


Blazing goIITian

Joined: 7 May 2007
Posts: 1724
11 Mar 2009 08:22:10 IST
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APPLY THE FORMULA 2 SINA COS B =SIN(A+B) + SIN(A-B)  IN RHS.

=>RHS=SIN(90+A+B) +SIN(A-B)

             =COS(A+B) + SIN(A-B) =LHS


Cool goIITian

Joined: 10 Mar 2009
Posts: 45
11 Mar 2009 09:41:49 IST
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cos(A+B)=sin(90-A-B)

sin(90-A-B) + sin(A-B) = 2sin(45+A)cos(45+B)

we know that sin(x) + sin(y)=2sin([x+y]/2)cos([x-y]/2)

 

so we get that

sin(90-A-B) + sin(A-B)=2sin(45-B)cos(45-A)

 

but we know that sin(45-B)=cos(90-(45-b))=cos(45+B) and cos(45-A)=sin(90-(45-A))=sin(45+A)

 

hence we get that

 

cos(A+B) + sin(A-B) = 2sin(45+A)cos(45+B)

 

do rate me.........


Cool goIITian

Joined: 10 Mar 2009
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11 Mar 2009 15:26:24 IST
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i have given each and every step perfectly....

 

wat else do u want..... plz give me full ratings.....


Blazing goIITian

Joined: 7 May 2007
Posts: 1724
18 Mar 2009 22:50:19 IST
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APPLY THE FORMULA 2 SINA COS B =SIN(A+B) + SIN(A-B)  IN RHS.

=>RHS=SIN(90+A+B) +SIN(A-B)

             =COS(A+B) + SIN(A-B) =LHS                                                          

PLSSSSSSSSSSSS      RATEEEEEEEEEEEEEEE




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