Question

Show that 2cos20 - 1 = 1.- 2sin?O.​

Answer 1

Given pair of equations 2sin

2

θ−cos2θ=0 and 2cos

2

θ−3sinθ=0

2sin

2

θ−cos2θ=0

⇒2sin

2

θ−(1−2sin

2

θ)=0

⇒4sin

2

θ=1

⇒sinθ=±

2

1

And 2cos

2

θ−3sinθ=0

⇒2(1−sin

2

θ)−3sinθ=0

⇒2sin

2

θ+3sinθ−2=0

⇒sinθ=

4

−3±

9+16

⇒sinθ=

4

−3±5

⇒sinθ=

2

1

as−1≤sinθ≤1

So sinθ=

2

1

satisfies both the equations

⇒θ=

6

π

,

6

5π

as θ∈[0,2π]