If `sin theta+sin2theta+sin3theta=sin alpha` and `cos theta+cos 2theta+cos3theta=cos alpha`, then `theta` is equal to

Question

If `sin theta+sin2theta+sin3theta=sin alpha` and `cos theta+cos 2theta+cos3theta=cos alpha`, then `theta` is equal to

If `sin theta+sin2theta+sin3theta=sin alpha` and `cos theta+cos 2theta+cos3theta=cos alpha`, then `theta` is equal to
A. `alpha//2`
B. `alpha`
C. `2alpha`
D. `alpha//6`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - C
`sin theta + sin 3theta sin 2theta = sin alpha`
`rArr 2sin 2theta cos theta + sin 2 theta = sin alpha`
`rArr sin 2th3eta (2cos theta+1) = sin alpha`
Now `cos theta + cos 3thetas + cos 2theta = cos alpha` …(1)
`2cos 2theta cos theta + cos theta + cos 2theta = cos alpha`
`cos 2theta (2cos theta + 1)=cos alpha` ....(2)
F?rom (1) and (2),
`tan 2theta = tan alpha rArr 2theta = alpha rArr theta =alpha//2`