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

Question

matimaticas · Answer

a. 1
b. 2
c. sin^2Θ
d. cos^2Θ

anonymous · Answer

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

luigi0210 · Answer

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

anonymous · Answer

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

matimaticas · Answer

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

luigi0210 · Answer

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

luigi0210 · Answer

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

luigi0210 · Answer

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

matimaticas · Answer

so it's B (2)?

luigi0210 · Answer

Yup yup ~

matimaticas · Answer

thanks :)