Answer:
cos(2theta) = 21/25
sin(2theta) = = 2sqrt(46)/25
Step-by-step explanation:
cos(2theta) = 1 - 2sin²(theta)
= 1 - 2(-sqrt(2)/5)²
= 1 - 2(2/25)
= 1 - 4/25
= 21/25
cos²(theta) = 1 - sin²(theta)
= 1 - (-sqrt(2)/5)²
= 1 - 2/25
cos²(theta) = 23/25
cos(theta) = - sqrt(23)/5
Sin(2theta) = 2sin(theta)cos(theta)
= 2 × (-sqrt(2)/5) × (-sqrt(23)/5)
= 2sqrt(46)/25
