Home
Class 12
MATHS
If cos alpha + cos beta + cos gamma = ...

If ` cos alpha + cos beta + cos gamma = 0 sin alpha + sin beta + sin gamma ` , Prove that
`cos^(2) alpha + cos^(2) beta + cos^(2) gamma = 3/2 = sin^(2) alpha + sin^(2) beta + sin^(2) gamma`.

Text Solution

Verified by Experts

The correct Answer is:
`3/2`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MODEL PAPER 7

    VGS PUBLICATION-BRILLIANT|Exercise SECTION - A (VERY SHORT ANSWER TYPE QUESTIONS)|10 Videos

  • MODEL PAPER 7

    VGS PUBLICATION-BRILLIANT|Exercise SECTION - B (SHORT ANSWER TYPE QUESTIONS)|7 Videos

  • MODEL PAPER 7

    VGS PUBLICATION-BRILLIANT|Exercise SECTION -B (SHORT ANSWER TYPE QUESTIONS)|7 Videos

  • MODEL PAPER 6

    VGS PUBLICATION-BRILLIANT|Exercise SECTION-C|7 Videos

  • MODEL PAPER 8

    VGS PUBLICATION-BRILLIANT|Exercise SECTION - C (LONG ANSWER TYPE QUESTIONS)|7 Videos

Similar Questions

Explore conceptually related problems

If cos alpha + cos beta + cos gamma =3 , " then " sin alpha + sin beta + sin gamma =

If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then show that cos 3 alpha + cos 3 beta + cos 3 gamma = 3 cos ( alpha + beta + gamma)

Knowledge Check

  • cos alpha + cos beta + cos gamma + cos ( alpha + beta + gamma ) =

    A
    `4 sin""((alpha + beta )/(2))* cos""((beta + gamma )/(2)) * cos ((gamma + alpha )/(2))`
    B
    `4 cos""((alpha + beta )/(2)) * cos""((beta + gamma )/(2)) * cos ""((gamma + alpha )/(2))`
    C
    `4 sin""((alpha + beta )/(2))* sin ((beta + gamma )/(2)) * sin""(( gamma + alpha )/(2))`
    D
    `4 cos ""((alpha + beta )/(2)) * cos""((beta + gamma )/(2))* sin""((gamma + alpha )/(2))`

  • If cos alpha + cos beta =0 = sin alpha + sin beta " then " cos (alpha - beta )=

    A
    0
    B
    `1`
    C
    `-1`
    D
    2

  • I : If cos alpha + cos beta + cos gamma =3 " then " sin alpha + sin beta + sin gamma =0 II : If sin alpha + sin beta + sin gamma =3 " then " cos alpha + cos beta + cos gamma =0

    A
    only I is true
    B
    only II is true
    C
    both I & II are true
    D
    neither I nor II are true

    • Similar Questions

    Explore conceptually related problems

    If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then show that cos ( alpha + beta) + cos ( beta + gamma) + cos ( gamma + alpha) = 0

    If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0 . Then Prove that cos^2alpha+cos^2beta+cos^2gamma=3/2=sin^2alpha+sin^2beta+sin^2gamma

    If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then show that sin 3 alpha + sin 3 beta + sin 3 gamma = 3 sin ( alpha + beta + gamma)

    If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0 . Then Prove that sin2alpha+sin2beta+sin2gamma=0

    If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0 . Then Prove that cos(alpha+beta)+cos(beta+gamma)+cos(gamma+alpha)=0

    Home
    Profile