Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

PROVE SIN2A+SIN2B-SINC=4COSACOSBSINC

 PROVE SIN2A+SIN2B-SINC=4COSACOSBSINC

Grade:12

2 Answers

Aman Bansal
592 Points
8 years ago

Dear bayana,

he double angle formula:
sin 2Θ = 2 sin Θ cos Θ

sin 2A + sin 2B - sin 2C
... = 2 sin A cos A + 2 sin B cos B - 2 sin C cos C 

Since A + B + C = π ;
A is a supplement angle of ( B + C )
B is a supplement angle of ( A + C )
C is a supplement angle of ( A + B )
TAKE NOTE that the sine of supplementary angles are equal !!!

sin 2A + sin 2B - sin 2C
... = 2 sin A cos A + 2 sin B cos B - 2 sin C cos C 
... = 2 sin ( B + C ) cos A + 2 sin ( A + C ) cos B - 2 sin ( A + B ) cos C

From the Sum of Angle Identity:
sin ( α + ß ) = sin α cos ß + cos α sin ß

sin 2A + sin 2B - sin 2C
... = 2 sin A cos A + 2 sin B cos B - 2 sin C cos C 
... = 2 sin ( B + C ) cos A + 2 sin ( A + C ) cos B - 2 sin ( A + B ) cos C
... = 2 ( sin B cos C + cos B sin C ) cos A 
..... ..... + 2 ( sin A cos C + cos A sin C ) cos B
..... ..... – 2 ( sin A cos B + cos A sin B ) cos C
... = 2 cos A sin B cos C + 2 cos A cos B sin C
..... ..... + 2 sin A cos B cos C + 2 cos A cos B sin C
..... ..... – 2 sin A cos B cos C – 2 cos A sin B cos C
... = 2 cos A cos B sin C + 2 cos A cos B sin C
... = 4 cos A cos B sin C

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple  to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert


rahul dahiya
18 Points
8 years ago

first of all ur question is wrong

 

 

its sin2a+sin2b-sin2c=4 cosa cosb sinc

applying SIN2X=2SINXCOSX

A+B+C=180

AND A IS SUPPLEMENT ANGLE OF (B+C)

B IS SUPLEMET OF (A+C) AND C OF (A+B)

 

WE GET

SIN2A+SIN2B+SIN2C=2SIN(B+C)COSA+2SIN(A+C)COSB-2SIN(A+B)COSC

NOW APPLYING SUM PROPERTY

SIN(X+Y)=SINX COSY + COSX SINY

AND SOLVING WE GET 4COSACOBSINC

 

 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free