Question

simplify without a calculator:
1 - 2\sin^{2}(15^{\circ})

Explanation:

Step1: Use double - angle formula

According to the double - angle formula for cosine $\cos(2\alpha)=1 - 2\sin^{2}\alpha$. Here $\alpha = 15^{\circ}$, so $1-2\sin^{2}(15^{\circ})=\cos(2\times15^{\circ})$.

Step2: Calculate the value

Calculate $2\times15^{\circ}=30^{\circ}$, and we know that $\cos(30^{\circ})=\frac{\sqrt{3}}{2}$.

Answer:

$\frac{\sqrt{3}}{2}$