Verified answer

(5sin(t) - 5cos(t))^2 = 25sin^2(t) - 50sin(t)cos(t) + 25cos^2(t) = 25(sin^2(t) + cos^2(t) - 2sin(t)cos(t))

= 25(1 - sin(2t))

(5 sin t − 5 cos t)^2 = 25sin^2 t + 25 cos^2 t - 50sin t cos t

I used (a - b)^2 = a^2 + b^2 - 2ab

= 25 - 50sintcost

( I used sin^2 t + cos^2 t = 1)

= 25(1 - 2sintcost)

and using sin 2t = 2sin t cos t

= 25 ( 1 - sin 2t)

5^2(sin t-cos t)^2=25(1-2sin t cos t)

25(1-sin 2t)

= 25(sin(t) -cos(t))^2

= 25(sin^2(t) - 2sin(t)cos(t) + cos^2(t))

= 25(1 - 2sin(t)cos(t))

= 25(1 - sin(2t))