Value of $$2 (sin^6 θ + cos^6 θ) - 3 (sin^4 θ + cos^4 θ) + 1 $$is

Expression : $$2 (sin^6 θ + cos^6 θ) - 3 (sin^4 θ + cos^4 θ) + 1 $$

= $$2[(sin^2 \theta)^3 + (cos^2 \theta)^3] - 3 (sin^4 \theta + cos^4 \theta) + 1$$

Using, $$a^3 + b^3 = (a + b)(a^2 + b^2 - ab)$$

= $$2[(sin^2 \theta + cos^2 \theta) (sin^4 \theta + cos^4 \theta - sin^2 \theta . cos^2 \theta)] - 3 (sin^4 \theta + cos^4 \theta) + 1$$

= $$2sin^4 \theta + 2cos^4 \theta - 2sin^2 \theta cos^2 \theta - 3sin^4 \theta - 3cos^4 \theta + 1$$

= $$-(sin^4 \theta + cos^4 \theta + 2sin^2 \theta cos^2 \theta) + 1$$

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

= -1 + 1 = 0