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

Given: $sin\theta-cos\theta=0$.

To do: To find the value of $sin^{4}\theta+cos^{4}\theta$.

$sin\theta-cos\theta = 0$

$\Rightarrow sin\theta= cos\theta$

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

$\Rightarrow tan\theta = 1$

As known, $tan45^{o} = 1$

So,

$tan\theta=tan45^{o}$

$\theta = 45^{o}$

$sin45^{o} = \frac{1}{\sqrt{2}}  cos45^{o} = \frac{1}{\sqrt{2}}$

$sin^{4}\theta+cos^{4}\theta  = ( \frac{1}{\sqrt{2}})^{4}+( \frac{1}{\sqrt{2}})^{4}$

                      $= \frac{1}{4}+\frac{1}{4} =\frac{2}{4} =\frac{1}{2} = 0.5$