If tan θ=( sin α- cos α/ sin α+ cos α), then sin α+ cos α and sin α- cos α must be equal to

Question

If tan θ=( sin α- cos α/ sin α+ cos α), then sin α+ cos α and sin α- cos α must be equal to (A) √2 cos θ, √2 sin θ (B) √2 sin θ, √2 cos θ (C) √2 sin θ, √2 sin θ (D) √2 cos θ, √2 cos θ

Tardigrade Admin · Accepted Answer

We have tan θ=( sin α- cos α/ sin α+ cos α) =( sin (α-(π/4))/ cos (α-(π)4)) ⇒ tan θ= tan (α-(π/4)) ⇒ θ=α-(π/4) ⇒ α=θ+(π/4) Put value of α and find sin α+ cos α=√2 cos θ and sin α- cos α=√2 sin θ

Q. If $tan θ = \frac{s i n α - c o s α}{s i n α + c o s α}$ , then $sin α + cos α$ and $sin α - cos α$ must be equal to

$2 cos θ, 2 sin θ$

$2 sin θ, 2 cos θ$

$2 sin θ, 2 sin θ$

$2 cos θ, 2 cos θ$

Q. If tanθ=sinα+cosαsinα−cosα​, then sinα+cosα and sinα−cosα must be equal to

2​cosθ,2​sinθ

2​sinθ,2​cosθ

2​sinθ,2​sinθ

2​cosθ,2​cosθ

We have tanθ=sinα+cosαsinα−cosα​ =cos(α−4π​)sin(α−4π​)​ ⇒tanθ=tan(α−4π​) ⇒θ=α−4π​ ⇒α=θ+4π​ Put value of α and find sinα+cosα=2​cosθ and sinα−cosα=2​sinθ

Q. If $tan θ = \frac{s i n α - c o s α}{s i n α + c o s α}$ , then $sin α + cos α$ and $sin α - cos α$ must be equal to

$2 cos θ, 2 sin θ$

$2 sin θ, 2 cos θ$

$2 sin θ, 2 sin θ$

$2 cos θ, 2 cos θ$