ft cot 2t pi4 VERIFY EACH OF TRIG IDENTITY 2 sinz X sin4

f(t) = -cot (2t - pi/4) VERIFY EACH OF TRIG IDENTITY: 2 sin^z X = sin^4 X - cos^4 X + 1 csc X/cot X + tan X = cos X

1. 2sin²x= sin⁴x-cos⁴x +1

Starting with the right side

sin⁴x-cos⁴x +1

(sin²x)²-(cos²x)²+1

(sin²x+cos²x)(sin²x-cos²x)+1

sin²x-cos²x+1

sin²x+sin²x=2sin²x which is equal to left side

2. cscx/(cot x + tan x) = cos x

Starting with the left side

cscx/(cotx + tanx)

1/sinx/(cosx/sinx + sinx/cosx)

1/sinx/((cos²x+sin²x))/sinx cos x

cos x/ 1=cos x that is equal to the right side