The value of 8(sin⁶θ + cos⁶θ) - 12(sin⁴θ + cos⁴θ) is equal to?

Solution (By Examveda Team)

$$\eqalign{ & {\text{8}}\left( {{{\sin }^6}\theta + {\text{co}}{{\text{s}}^6}\theta } \right) - {\text{12}}\left( {{{\sin }^4}\theta + {\text{co}}{{\text{s}}^4}\theta } \right) \cr & {\text{Put }}\theta = {0^ \circ } \cr & = 8\left( {{{\sin }^6}{0^ \circ } + {{\cos }^6}{0^ \circ }} \right) - 12\left( {{{\sin }^4}{0^ \circ } + {{\cos }^4}{0^ \circ }} \right) \cr & = 8\left( {0 + 1} \right) - 12\left( {0 + 1} \right) \cr & = - 4 \cr} $$