Question

The greatest value of ${\sin }^4\theta +{\cos }^4\theta$ is

• A. $\frac{1}{2}$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

$1$

${\sin }^4\theta +{\cos }^4\theta ={({\sin }^2\theta +{\cos }^2\theta )}^2-2{\sin }^2\theta {\cos }^2\theta$

$=1-\frac{1}{2}({\sin }^{2}2\theta {)}^2$

[$\because co{s}^2\theta +si{n}^2\theta =1andminimumvalueofsi{n}^{2}2\theta is0]$

${\sin }^4\theta +{\cos }^4\theta$

$=1-0$

${\sin }^4\theta +{\cos }^4\theta$ = $1$