Question

Simplify: (sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2

Answer 1

a. 1
b. 2
c. sin^2Θ
d. cos^2Θ

Answer 2

sin^2(x) + cos^2(x) -cosx*sin(x) +sin^2(x) + cos^2(x) +cos(x)*sin(x)=
2*sin^2(x) + 2 *cos^2(x)= 2

Answer 3

Did you trying distributing? Also use: \(\Large sin^2 \theta +cos^2\theta=1\)

Answer 4

you have to know sin^2(x) + cos^2(x) = 1

Answer 5

@Luigi0210 I got the second expression to be 1, but idk about the 1st expression

Answer 6

Distribute it: \(\Large (sin\theta-cos\theta)^2=sin^2\theta-2cos\theta sin\theta+cos^2\theta\)

Answer 7

Like @borak said, it'll end up being 2
There will be \(\Large sin^2\theta+cos^2\theta+sin^2\theta+cos^2\theta+2cos\theta sin\theta-2cos\theta sin\theta\)

Answer 8

The sin's and cos's squared will add up, and the 2cos sin will cancel when distributed

Answer 9

so it's B (2)?

Answer 10

Yup yup ~

Answer 11

thanks :)