Question

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
A. `sin(a+ b+ gamma)`
B. `3 sin (alpha + beta + gamma)`
C. ` 18 sin(alpha + beta + gamma)`
D. `sin(alpha+ beta + gamma)`

Answer 1

Correct Answer - C
Let `a=cosalpha+isinalpha`
`b=cosbeta+isinbeta`
`c=cosgamma+isingamma`
Then, `a+2b+3c=(cosalpha+2cosbeta+3cosgamma)+i(sinalpha+2sinbeta-3singamma)=0`
`rArr a^(3)+8b^(2)+27c^(2)=18abc`
`rArr cos3alpha+8 cos3beta+27 sin3gamma=18cos(alpha+beta+gamma)`
and `sin3alpha+8 sin3beta+27 sin3gamma=18 sin(alpha+beta+gamma)`