Home
Class 12
MATHS
Prove by vector method that cos(A+B)=c...

Prove by vector method that `cos(A+B)=cos AcosB-sinAsinBdot`

Text Solution

Verified by Experts

Let `hati and hatj` be unit vectors along OX and OY, respectively.
Let `vecOP.vecOQ` be two unit vectors drawn in the plane XOY such that.
`angleXOP=A , angleXOQ= B`
POQ= A+B
now `vecOP = hati cos A+hatj sin A`
`vecOQ=hati cos B + hatj sin B`
`vecOP.vecOQ= cosA cosB-sinA sinB`
`(1) (1) cos (A+B)=cosA cosB -sin B - sin A sinB`
`cos (A+B) = cos AcosB-sinA sinB`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.1|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.2|15 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

cos(A + B) cos (A-B) =

If A,B,(A - B)are positive acute angles, then prove that geometrically : cos (A - B) = cos A cos B + sin A sin B

Prove that a cos A + b cos B + c cos C = 4 R sin A sin B sin C.

Prove that in triangle A B C ,cos^2A+cos^2B-cos^2C=1-2sinAsinBcosCdot

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

In a DeltaABC .Prove that cos (A+B)+cosC=0.

Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B\ cos C

Prove that (sin A-sin B)/(cos A+ cos B) = "tan" (A-B)/2

Prove that cos(60^(@)+A) + cos(60^(@)-A)-cosA=0

In /_\ABC ,Prove that a cos A + b cos B + c cos C = 2a sin B sin C