Question

If $si{n}^4\theta +co{s}^4\theta =1-\frac{1}{2}f\left(\theta \right)$ then $f\left(\frac{\pi }{4}\right)=$

• A. 1
• B. 0
• C. 1/2
• D. 1/4

Answer 1

The correct option is A 1

From above ${\sin }^4\theta +{\cos }^4\theta =1-\frac{f\left(\theta \right)}{2}$

$f\left(\theta \right)=(1-{\sin }^4\theta -{\cos }^4\theta )2$

$f\left(\frac{\pi }{4}\right)=(1-{\sin }^4\frac{\pi }{4}+{\cos }^4\frac{\pi }{4}).2$

$=(1-{\left(\frac{1}{\sqrt{2}}\right)}^4-{\left(\frac{1}{\sqrt{2}}\right)}^4)2$

$=(1-\frac{1}{4}-\frac{1}{4})\times 2$

$=(1-\frac{1}{2})\times 2=\frac{1}{2}\times 2$

$f\left(\theta \right)=1$