$$sin^6\theta + cos^6\theta$$​ can be simplified as:

Correct option is D

Given:

​$$sin^6\theta + cos^6\theta$$​​

Formula Used:

​$$\sin^2 \theta + \cos^2 \theta = 1$$​​

​$$a^3+b^3 = (a+b)(a^2 + b^2 -ab)$$​​

Solution:

​$$sin^6\theta + cos^6\theta$$​​

​$$(\sin^2 \theta)^3 + (\cos^2 \theta)^3$$​​

​$$= (\sin^2 \theta + \cos^2 \theta)((\sin^2 \theta)^2 + (\cos^2 \theta)^2 - \sin^2\theta \cos^2 \theta)$$​​

​$$= (1)((\sin^2 \theta)^2 + (\cos^2 \theta)^2 - \sin^2\theta \cos^2 \theta +2\sin^2\theta \cos^2 \theta-2\sin^2\theta \cos^2 \theta )$$​​

​$$=((\sin^2 \theta+ \cos^2 \theta)^2 -3\sin^2\theta \cos^2 \theta )$$​​

​$$=((1)^2 -3\sin^2\theta \cos^2 \theta )$$​​

​$$=(1 -3\sin^2\theta \cos^2 \theta )$$​​