Home
Class 12
MATHS
If cos alpha+cos beta+cos gamma=0=sin al...

If `cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma`, then `(sin3alpha+sin3beta+sin3gamma)/(sin(alpha+beta+gamma))` is equal to

A

`1`

B

`-1`

C

`3`

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
C
`(a)` `a=e^(ialpha)`, `b=e^(ibeta)`, `c=e^(igamma)`
Clearly `a+b+c=0`
`impliesa+b+c=0=(1)/(a)+(1)/(b)+(1)/(c )`
`impliesa^(3)+b^(3)+x^(3)=3abc`
`impliessin3alpha+sin3beta+sin3gamma=sin(alpha+beta+gamma)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|11 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|101 Videos

Similar Questions

Explore conceptually related problems

If sin alpha+ sin beta+ sin gamma=3, then sin^3alpha+sin^3beta+sin^3 gamma=

If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 , then the value of sin3alpha+8sin3beta+27sin3gamma is sin(a+b+gamma) b. 3sin(alpha+beta+gamma) c. 18"sin"(alpha+beta+gamma) d. sin(alpha+2beta+3)

If cos alpha + cos beta + cos gamma = 0 and also sin alpha + sin beta + sin gamma= 0, then prove that: cos 3 alpha + cos 3beta + cos 3gamma = 3 cos (alpha + beta + gamma)

If cos alpha + 2 cos beta +3 cos gamma = sin alpha + 2 sin beta + 3 sin gamma y = 0 , then the value of sin 3alpha + 8 sin 3beta + 27 sin 3gamma is

If 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and gamma are in

Let A and B denote the statements A : cos alpha + cos beta + cos gamma =0 B : sin alpha + siin beta + sin gamma = 0 If cos(beta - gamma) + cos (gamma -alpha) + cos (alpha -beta) = - (3)/(2) , then

Given alpha+beta-gamma=pi, prove that sin^2alpha+sin^2beta-sin^2gamma=2sinalphasinbetacosgammadot

If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma , then which of the following is/are true:- (a) cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-3/2 (b) cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-1/2 (c) sumcos2alpha+2cos(alpha+beta)+2cos(beta+gamma)+2cos(gamma+alpha)=0 (d) sumsin2alpha+2sin(alpha+beta)+2sin(beta+gamma)+2sin(gamma+alpha)=0

If cos^(-1) alpha + cos^(-1) beta + cos^(-1) gamma = 3pi , then alpha (beta + gamma) + beta(gamma + alpha) + gamma(alpha + beta) equal to