Cos420°.Cos390°+Sin(-300°).Sin(-330°) এর মান কত?

Cos420°.Cos390°+Sin(-300°).Sin(-330°) এর মান নির্ণয়:

আমরা জানি, \(cos(360° + θ) = cosθ\) এবং \(sin(-θ) = -sinθ\)

সুতরাং,

\(cos420° = cos(360° + 60°) = cos60° = \frac{1}{2}\) 😊

\(cos390° = cos(360° + 30°) = cos30° = \frac{\sqrt{3}}{2}\) 😎

\(sin(-300°) = -sin300° = -sin(360° - 60°) = -(-sin60°) = sin60° = \frac{\sqrt{3}}{2}\) 😉

\(sin(-330°) = -sin330° = -sin(360° - 30°) = -(-sin30°) = sin30° = \frac{1}{2}\) 🤩

অতএব, \(cos420°.cos390° + sin(-300°).sin(-330°) = (\frac{1}{2}).(\frac{\sqrt{3}}{2}) + (\frac{\sqrt{3}}{2}).(\frac{1}{2})\)

\(= \frac{\sqrt{3}}{4} + \frac{\sqrt{3}}{4} = \frac{2\sqrt{3}}{4} = \frac{\sqrt{3}}{2}\) 🥳

সুতরাং, Cos420°.Cos390°+Sin(-300°).Sin(-330°) এর মান \( \frac{\sqrt{3}}{2} \)।