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

How does cos^2A+cos^2B+cos^2C+2cosAcosBcosC=1,where A,B,C are angles of triangles?

How does cos^2A+cos^2B+cos^2C+2cosAcosBcosC=1,where A,B,C are angles of triangles?

Grade:12

2 Answers

Rathod Shankar AskiitiansExpert-IITB
69 Points
10 years ago

   Dear Aparna Tiwari,       

 

          2cosAcosBcosC =(2cosAcosB)cosC                               here A+B+C=pi=∏       thereforen  C=pi-(A+B)
                                =(cos(A + B) + cos(A - B))cosC
                                =cos(pi - C)cosC + cos(A - B)cos(pi - (A + B))
                                =-2cos^2C - 2cos(A + B)cos(A - B)

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

 

cos^2A+cos^2B+cos^2C+2cosAcosBcosC=cos^2A+cos^2B+cos^2C-cos^2C - cos^2A + sin^2B

                                                                              =   cos^2B+ sin^2B =1

 

 


Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..



Askiitians Expert

Rathod Shankar Singh

IIT Bombay

 

Lab Bhattacharjee
121 Points
3 years ago
As cos(A+B)=cos(pi-C)=-cos Cπ2
 
cos^2A+cos^2B+cos^2C=1+\cos^2A-\sin^2B+\cos^2C=1+cos(A+B)cos(A-B)+cos^2C=1-cos C cos(A-B)-cos C cos(A+B)
 
=1-cos C[cos(A+B)+cos(A-B)]=1-cos C(2ocs Acos B)

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