Bài tập 8 trang 17 SGK Toán 11 NC

Với k ∈ Z ta có :

a) f(x) = −sin²x

f(x+kπ) = −sin²(x+kπ) = −[(−1)^ksinx]² = −sin²x = f(x)

b) f(x) = 3tan²x+1

f(x+kπ) = 3tan²(x+kπ)+1 = 3tan²x+1 = f(x)

c) f(x) = sinxcosx

f(x+kπ) = sin(x+kπ).cos(x+kπ) = (−1)^ksinx.(−1)^kcosx = sinxcosx = f(x)

d)

\(\begin{array}{*{20}{l}}
{f\left( x \right) = \sin x.\cos x + \frac{{\sqrt 3 }}{2}\cos 2x}\\
\begin{array}{l}
f\left( {x + k\pi } \right) = \sin \left( {x + k\pi } \right)\cos \left( {x + k\pi } \right)\\
 + \frac{{\sqrt 3 }}{2}\cos \left( {2x + k2\pi } \right)
\end{array}\\
\begin{array}{l}
 = {\left( { - 1} \right)^k}\sin x{\left( { - 1} \right)^k}\cos x + \frac{{\sqrt 3 }}{2}\cos 2x\\
 = \sin x.\cos x + \frac{{\sqrt 3 }}{2}\cos 2x = f\left( x \right)
\end{array}
\end{array}\)

-- Mod Toán 11 HỌC247