Question

2 cos theta+ 4 sin theta + cos 2 theta - sin 2 theta = 3 .find general solutions​

Answer 1

Step-by-step explanation:

3−2cosθ−4sinθ−cos2θ+sin2θ=0

⇒3−2cosθ−4sinθ−1+2sin

2

θ+2sinθcosθ=0

⇒2sin

2

θ−2cosθ−4sinθ+2sinθcosθ+2=0

⇒(sin

2

θ−2sinθ+1)+cosθ(sinθ−1)=0

⇒(sinθ−1)[sinθ−1+cosθ]=0

Case 1: Either sinθ=1

⇒θ=2nπ+π/2 where n∈l

Case 2: Or, sinθ+cosθ=1

⇒cos(θ−π/4)=cos(π/4)

⇒θ−π/4=2nπ±π/4

⇒θ=2nπ,2nπ+π/2 where n∈l

Hence, θ=2nπ,2nπ+π/2.