Question

If $(\sin \theta -\cos \theta )=0$, then $({\sin }^4\theta +{\cos }^4\theta )=$

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

The correct option is B $\frac{1}{2}$

$\sin \theta -\cos \theta =0$

$\sin \theta =\cos \theta$

$\frac{\sin \theta }{\cos \theta }=1$

$\tan \theta =1$

We know that $\tan \mathring{45=1}$

$so,\theta =\mathring{45}$

$\left({\sin }^4\theta +{\cos }^4\theta \right)$

$\left({\sin }^4\mathring{45}+{\cos }^4\mathring{45}\right)$ $=\{{\left(\frac{1}{\sqrt{2}}\right)}^4+{\left(\frac{1}{\sqrt{2}}\right)}^4\}$

$=\{\frac{1}{4}+\frac{1}{4}\}$

$=\frac{2}{4}=\frac{1}{2}$