Answer:
0.6472
Step-by-step explanation:
sinx + cosx = 2/5
(sinx + cosx)² = (2/5)²
sin²x + cos²x + 2sinxcosx = 4/25
1 + 2sinxcosx = 4/25
2sinxcosx = 4/25 - 1 = -21/25
sinxcosx = -21/50
(sinx + cosx)⁴ = (2/5)⁴
sin⁴x + cos⁴x + 4sinxcosx(sin²x + cos²x) + 6(sinxcosx)² = 16/625
sin⁴x + cos⁴x + 4*(-21/50)*1 + 6(21/50)² = 16/625
so
sin⁴x + cos⁴x = 16/625 + 84/50 - 6(21/50)² = -2.6728
sin⁴x + cos⁴x = 0.6472
