Question

Simplify: (sin theta - cos theta)^2 - (Sin theta + cos theta)^2

Answer 1

\[(\sin \theta -\cos \theta)^2\] is same as \[(\sin \theta -\cos \theta )(\sin \theta -\cos \theta)\]
Foil!

Answer 2

is the the answer -4sin theta cos theta?

Answer 3

i would like to see the work 2! :)

Answer 4

Using foil I get sin^2 theta - 2sin theta cos theta + cos^2 theta -( sin^2 theta +2 sin theta cos theta + cos^2 theta)

Answer 5

very good :=))

Answer 6

Thanks!

Answer 7

yw! gO_Od job! :)

Answer 8

\((\sin \theta - \cos \theta)^2 - (\sin \theta + \cos \theta)^2\)

\(=\sin^2 \theta - 2\sin \theta \cos \theta + \cos^2 \theta - (\sin^2 \theta + 2\sin \theta \cos \theta + \cos^2 \theta)\)

\(=\sin^2 \theta - 2\sin \theta \cos \theta + \cos^2 \theta - \sin^2 \theta - 2\sin \theta \cos \theta - \cos^2 \theta\)

\(=\color{red}{\sin^2 \theta} - 2\sin \theta \cos \theta + \color{green}{\cos^2 \theta }\color{red}{- \sin^2 \theta} - 2\sin \theta \cos \theta \color{green}{- \cos^2 \theta}\)

\(=\cancel{\color{red}{\sin^2 \theta}} - 2\sin \theta \cos \theta + \cancel{\color{green}{\cos^2 \theta }}\color{red}{- \cancel{\sin^2 \theta}} - 2\sin \theta \cos \theta \color{green}{- \cancel{\cos^2 \theta}}\)

\(= - 2\sin \theta \cos \theta - 2\sin \theta \cos \theta\)

\(= - 4\sin \theta \cos \theta\)

Answer 9

(sin ø - cos ø)^2 - (sin ø + cos ø)^2
= (1 - sin 2ø) - (1 + sin 2ø)
= - 2 sin 2ø
= -4 sin ø cos ø