Question

If $\sin A-\cos A=0$, then find the value of ${\sin }^{4}A+{\cos }^{4}A$.

Answer 1

$\sin A-\cos A=0$

$\Rightarrow A=\cos A$

$\Rightarrow \tan A=1$

$\Rightarrow A=\frac{\pi }{4}$

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