Question

Evaluate

sin60° • cos30° - cos30° • sin30°​

Answer 1

1

Hope it's helpful to you

Answer 2

To Find :

• sin60° • cos30° - cos30° • sin30°

⠀ ⠀⠀ ⠀ ⠀⠀ ⠀

Solution :

sin60° • cos30° - cos30° • sin30°

sin60° × cos30° - cos30° × sin30°

⠀ ⠀⠀ ⠀

By substituting the values of :

• sin60° = $\sf \dfrac{\sqrt{3}}{2}$
• cos30° = $\sf \dfrac{\sqrt{3}}{2}$
• sin30° = $\sf \dfrac{1}{2}$

⠀ ⠀⠀ ⠀

$\sf : \implies \dfrac{\sqrt{3}}{2} \times \dfrac{\sqrt{3}}{2} - \dfrac{\sqrt{3}}{2} \times \dfrac{1}{2}$

$\sf : \implies \dfrac{\sqrt{3} \times \sqrt{3}}{2 \times 2} - \dfrac{\sqrt{3} \times 1}{2\times 2}$

$\sf : \implies \dfrac{(\sqrt{3})^{2}}{4} - \dfrac{\sqrt{3}}{4}$

$\sf : \implies \dfrac{3}{4} - \dfrac{\sqrt{3}}{4}$

$\sf : \implies \dfrac{3 - \sqrt{3}}{4}$

⠀ ⠀⠀ ⠀

Hence, value of sin60° • cos30° - cos30° • sin30° is :

• $\bf \dfrac{3 - \sqrt{3}}{4}$