simplify without a calculator:\n1 - 2\\sin^{2}(15^{\\circ})
simplify without a calculator:\n1 - 2\\sin^{2}(15^{\\circ})
Answer
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:
$\frac{\sqrt{3}}{2}$