If sin$$\phi$$ - cos$$\phi$$ = 0, then the value of sin$$^4 \phi$$ + cos$$^4 \phi$$ + tan$$^2 \phi$$ is:​

Correct option is D

Given: 

sin$$\phi$$ - cos$$\phi$$ = 0,   

Value Used: 

​$$cos45^0 = \frac{1}{\sqrt2}\\\ \\sin45^0 = \frac{1}{\sqrt2}\\\ \\tan45^0 = 1$$​​

Solution: 

sin$$\phi$$ - cos$$\phi$$ = 0,  

sin$$\phi$$ =  cos$$\phi$$ 

$$\phi= 45^0$$​   

Then, 

The value of sin$$^4 \phi$$ + cos$$^4 \phi$$ + tan$$^2 \phi$$ 

 =  sin$$^4 \phi$$ + cos$$^4 \phi$$ + tan$$^2 \phi$$ 

 $$= sin^4 \phi +cos^4 \phi +tan^4 \phi \\\ \\ = sin^4 45^0 +cos^4 45^0 +tan^4 45^0 \\\ \\= (\frac{1}{\sqrt2})^4 + (\frac{1}{\sqrt2})^4 + (1)^4 \\\ \\= \frac{1}{4}+\frac{1}{4} + 1 \\\ \\= \frac{(1+1)}{4} + 1 \\\ \\ = \frac{1}{2} + 1 \\\ \\= \frac{3}{2}$$