Home
Class 11
MATHS
Prove that cos(x+y)=cosxcosy-sinxsiny...

Prove that `cos(x+y)=cosxcosy-sinxsiny`

Text Solution

Verified by Experts

Acc to the figure
`AC^2 = sqrt((1 - cos(x+y))^2 + ( 0 - sin(x+y)^2)) `
`= sqrt(1+ cos^2 (x+y) - 2cos(x+y) + sin^2(x+y))`
`= sqrt(2-2cos(x+y))`
`AC^2 = 2-2cos(x+y)`
`BD^2 = (cos x - cos y)^2 + (sin x + sin y)^2`
`cos^2 x + cos^2y- 2cosx cos y + sin^2 x + sin^2 y + 2 sinx siny`
`= 2 + 2sinx sin y - 2cos xcos y`
...
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Prove geometrically that cos (x+y)= cosx.cosy- sinx.siny and hence show that cos2x=cos^2x-sin^2x .

Prove that geometrically that cos (x+y)= cosx.cosy-sinx.siny and hence show that cos2x=cos^2x-sin^2x .

Knowledge Check

  • The 2 triangle in the figure above share a common side. What is cos(x+y) ("Note : "cos (x+y)=cos xcosy-sinxsiny" for all x and y.")

    A
    `(4)/(5)`
    B
    `(3+4sqrt(24))/(5)`
    C
    `(4sqrt(24)-3)/(25)`
    D
    `(3-4sqrt(24))/(25)`

    • Similar Questions

    Explore conceptually related problems

    Prove geometrically that cos(x + y) = cos x cos y - sinx sin y and hence prove cos((pi)/(2) + x) = - sin x .

    Prove that (cos x-cos y)^(2)+(sin x-sin y)^(2)=4 sin ^(2)((x-y)/(2))

    Prove that: (cos x+cos y)^(2)+(sin x-sin y)^(2)=4cos^(2)backslash(x+y)/(2)

    Prove that (cos x +cos y)^(2)+(sin x-sin y)^(2)=4 cos^(2) ((x+y)/(2))

    Prove that: cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)

    Prove that cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)

    Prove that cos ^ (- 1) ((cos x + cos y) / (1 + cos x cos y)) = 2tan ^ (- 1) (tan ((x) / (2)) tan ((y) / (2)))

    Home
    Profile