Home
Class 11
MATHS
Prove that: cos^2A+cos^2B-2cosA\ cos B c...

Prove that: `cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)`

Text Solution

AI Generated Solution

To prove the identity \( \cos^2 A + \cos^2 B - 2 \cos A \cos B \cos(A + B) = \sin^2(A + B) \), we will follow these steps: ### Step 1: Start with the left-hand side We begin with the left-hand side of the equation: \[ \cos^2 A + \cos^2 B - 2 \cos A \cos B \cos(A + B) \] ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|167 Videos
  • TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|193 Videos

Similar Questions

Explore conceptually related problems

If A+B+C= 360^(@) ,prove that: 1-cos^(2)A-cos^(2)B-cos^(2)C+2cosA cos B cos C=0

If A+B+C=2pi , prove that : cos^2B+cos^2C-sin^2A-2cosA cosB cosC=0 .

If A+B+C=180, prove that cos^(2)A+cos^(2)B+cos^(2)C=1-2cos A cos B cos C

If A+B+C=180^0 , prove that : cos^2 A + cos^2 B + cos^2 C + 2cosA cosB cosC=1 .

If A+B+C=pi , prove that : cosA + cosB-cosC=4cos(A/2) cos(B/2) sin(C/2) -1

Prove that: sin^(2)A=cos^(2)(A-B)+cos^(2)B-2cos(A-B)cos A cos B

If A+B+C=2 pi, then prove that cos^(2)B+cos^(2)C-sin^(2)A=2cos A cos B cos C

If A+B+C=0 , Prove : cos^2 A + cos^2 B +cos^2 C=1+2cosA cosB cosC .

If A+B+C=pi, prove that cos 2A-cos 2B-cos 2C=-1+4cos A sinBsinC

If A+B+C=180^0 , prove that : cos^2(A/2) + cos^2(B/2) - cos^2(C/2) = 2cos(A/2) cos(B/2) sin( C/2)