Question

Find the distance between the points:
(cosθ, sinθ) and (sinθ, cosθ)

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

We know that,

$\Large{\implies{\boxed{\boxed{\sf{Distanve = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}}}}$

Where,

• x1 = Cos θ
• x2 = Sin θ
• y1 = Cos θ
• y2 = Sin θ

______________[Put Values]

$\sf{→ Distance = \sqrt{(Sin \: θ - Cos \: θ)^2 +( Sin \: θ - Cos \: θ)^2}} \\ \\ \Large{\implies{\boxed{\boxed{\sf{(a - b)^2 = a^2 + b^2 - 2ab}}}}} \\ \\ \sf{→ Distance = \sqrt{Sin^2 θ + Cos^2θ - 2Sinθ \: Cosθ +Sin^2 θ + Cos^2θ - 2Sinθ \: Cosθ}} \\ \\ \Large{\star{\boxed{\sf{Sin^2θ + Cos^2θ = 1}}}} \\ \\ \sf{→ Distance = \sqrt{1 - 2Sinθ \: Cosθ + 1 - 2Sinθ \: cos θ}} \\ \\ \sf{→ Distance = \sqrt{2 - 4Sin θ \: Cosθ}} \\ \\ \sf{→ Distance = \sqrt{2(1 - 2Sinθ \: Cosθ)}}$