Question

Find the maximum value of ${\sin }^{113}\theta \cdot {\cos }^{113}\theta$.

• A. ${\left(\frac{3}{2}\right)}^{113}$
• B. $1$
• C. ${\left(\frac{1}{4}\right)}^{113}$
• D. ${\left(\frac{1}{2}\right)}^{113}$

Answer 1

The correct option is D ${\left(\frac{1}{2}\right)}^{113}$

${\sin }^{113}\theta \cdot {\cos }^{113}\theta$
Maximum value of ${\sin }^n\theta {\cos }^n\theta ={\left(\frac{1}{2}\right)}^n$
Hence, the greatest value of ${\sin }^{113}\theta \cdot {\cos }^{113}\theta ={\left(\frac{1}{2}\right)}^{113}$.