Вычислите: cos2a-cos6a, если cosa=1 / √2

Cos2a-cos6a=-2sin4a*sin2a=

=-8sinacosacos2a*sin2a=

=-8sina * cosa * cos2a*2sina * cosa=

=-16sin²a*cos²a*cos2a=

=-16sin²a*cos²a * (2cos²a-1) =

=-32sin²a*cos⁴a+16sin²a*cos²a

поскольку дано cosa=1/√2, то

sina=1/√2

-32 (1/√2) ² (1√2) ⁴+16 (1/√2) ² (1/√2) ²=

=-4+4=0

Ответ: 0.

cosa=1/√2 cos²a=1/2

sina=√1-1/2=1/√2 sin²a=1/5

cos2a=cos²a-sin²a=1/2-1/2=0

sin2a=2sinacosa=2*1/√2*1/√2=1

cos2a-coa6a=-2sin (-2a) sin4a=2sin2asin4a=2sin2a*2sin2acos2a=

=4sin²2acos2a=4 * 1*0=0