What is expand (cos(2pit)-1)(sin(2pit)+1) ?

The solution to expand (cos(2pit)-1)(sin(2pit)+1) is cos(2pit)sin(2pit)+cos(2pit)-sin(2pit)-1

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expand (cos(2pit)-1)(sin(2pit)+1)

expand

(cos (2 π t) - 1) (sin (2 π t) + 1)

cos (2 π t) sin (2 π t) + cos (2 π t) - sin (2 π t) - 1

Solution steps

(cos (2 π t) - 1) (sin (2 π t) + 1)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = cos (2 π t), b = - 1, c = sin (2 π t), d = 1

= cos (2 π t) sin (2 π t) + cos (2 π t) \cdot 1 + (- 1) sin (2 π t) + (- 1) \cdot 1

Apply minus-plus rules

+ (- a) = - a

= cos (2 π t) sin (2 π t) + 1 \cdot cos (2 π t) - 1 \cdot sin (2 π t) - 1 \cdot 1

Simplify

cos (2 π t) sin (2 π t) + 1 \cdot cos (2 π t) - 1 \cdot sin (2 π t) - 1 \cdot 1 : cos (2 π t) sin (2 π t) + cos (2 π t) - sin (2 π t) - 1

= cos (2 π t) sin (2 π t) + cos (2 π t) - sin (2 π t) - 1

A (2, - 1, 3) B (1, - 2, - 3)

e^{t} (- t e^{- t} - e^{- t})

\frac{2 s + 1}{( s ^{2} + 4 s + 3 ) ( s - 2 )}

\frac{d}{d t} ((x) (9 + sin (x)))

\frac{2 ( x + h ) + 3}{x + h - 1}

What is expand (cos(2pit)-1)(sin(2pit)+1) ?
The solution to expand (cos(2pit)-1)(sin(2pit)+1) is cos(2pit)sin(2pit)+cos(2pit)-sin(2pit)-1