Question

Help with planning strategies for trig functions

Answer 1

What would be the best first step in verifying the following identity? sin^4θ − cos^4θ = 1 − 2cos^2θ

My choices are:

Start with the right side of the equation by applying a form of the Pythagorean identity.

Start with the left side of the equation by applying a form of the Pythagorean identity.

Start with the left side of the equation by factoring it.

Start with the right side of the equation by multiplying bycos2θ.

Answer 2

Would we do start the left side of the equation by applying a form of the Pythagorean identity? because cos^2(x)+sin^2(x)=1?.

Answer 3

I dont know if I would be right though s:

Answer 4

well you could write sin^2(x) as 1-cos^2(x)
\[(1-\cos^2(x))^2-\cos^4(x)= 1-2\cos^2(x)+\cos^4(x)-\cos^4(x)\]

Answer 5

\[\text{ but I think factoring works too } \\ \sin^4(\theta)-\cos^4(\theta) \\ =(\sin^2(\theta)-\cos^2(\theta))(\sin^2(\theta)+\cos^2(\theta)) \\ =(\sin^2(\theta)-\cos^2(\theta))(1) \\ =(1-\cos^2(\theta))-\cos^2(\theta)\]

Answer 6

so that is kinda a weird question since you have two choices that sounds good to me

Answer 7

sorry it would't let me load S:

Answer 8

hmm which would you think would be the best way?

Answer 9

I guess go with applying Pythagorean first

Answer 10

if I could I would select both and show the teacher both ways

Answer 11

I say the way you suggested because maybe that seems like a step shorter I guess
it just depends what you consider a step :p

Answer 12

loool Thank you again :p just doing like practice problems for this stuff

Answer 13

just making sure i understand this

Answer 14

:)