Cos (a - π / 4) = 1 / 4, then sin2a

Cos (a - π / 4) = 1 / 4, then sin2a

cos(a-π/4)=cosacosπ/4+sinasinπ/4=√2/2cosa+√2/2sina=√2/2(cosa+sina)=1/4sina+cosa=√2/4sin2a=2sinacosa=(sina+cosa)²-(sin²a+cos²a)=1/8-1=-7/8

If cos (a-pie / 4) = 1 / 4, the value of sin2a is?

Because cos (a-pie / 4) = 1 / 4
Then cosacos (π / 4) + sinasin (π / 4) = 1 / 4
Cosa + Sina = root 2 of 4
(Sina) ^ 2 + (COSA) ^ 2 + 2sinacosa = 1 / 8
And (Sina) ^ 2 + (COSA) ^ 2 = 1
Then 2sinacosa = - 7 / 8
That is sin2a = - 7 / 8

1-sin2a-cos^2(a-π/4)

1-sin2a-cos^2(a-π/4)
=sin^2(a-π/4)-sin2a
=(radical 2sina - radical 2cosa) ^ 2-sin2a
=2(cosa^2-2sinacosa+cosa^2)-sin2a
=2(1-sin2a)-sin2a
=2-3sin2a