Question

The system of equations (cos 20)x + 4y +3z =0,2x+7y+7z =0, (sin 30)x – y + z = 0 has non trivial
solution then sin 30 + 2 cos 20 =
1)​

Answer 1

Answer:

Given system has non-trivial solution.

⇒

∣

∣

∣

∣

∣

∣

∣

∣

sin3θ

cos2θ

2

−1

4

7

1

3

7

∣

∣

∣

∣

∣

∣

∣

∣

=0

⇒7sin3θ+7cos2θ−6+7cos2θ−8=0

⇒sin3θ+2cos2θ=2

3sinθ−4sin

3

θ+2(1−2sin

2

θ)=2

−sinθ(4sin

2

θ+4sinθ−3)=

⇒sinθ=0 and sinθ=

2

1

∴θ=nπ and θ=nπ+(−1)

n

π/6;n∈Z

Hence, options A and B.

December 30, 2019