Question

cos60°×cos30°-sin60°×sin30°​

Answer 1

$\huge\underline{\bf{Given}}$

• Cos60° × Cos30° - Sin60° × Sin30°

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$\huge\underline{\bf{To\: find}}$

• Value of the given expression.

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$\huge\underline{\bf{Solution}}$

• According to the trigonometric table

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$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\bf{\bigstar{Trigonometric\: Table{\bigstar}}}}$

$\bullet\:\sf Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}$

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★ Putting values

$\tt\longmapsto{\dfrac{1}{2} \times \dfrac{\sqrt{3}}{2} - \dfrac{\sqrt{3}}{2} \times \dfrac{1}{2}}$

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$\tt\longmapsto{\dfrac{\sqrt{3}}{4} - \dfrac{\sqrt{3}}{4}}$

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$\tt\longmapsto{0}$

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Hence,

→ Cos60° × Cos30° - Sin60° × Sin30° = 0

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