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chaotic_butterflies
 one year ago
(sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2
I've worked this out multiple times, and my answer isn't a possible choice...
chaotic_butterflies
 one year ago
(sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2 I've worked this out multiple times, and my answer isn't a possible choice...

This Question is Closed

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Answer choices: A) 1 B) 2 C) sin^2 theta D) cos^2 theta

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1show ur work please :)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1remember these two formulas \[\huge\rm (a+b)^2 = a^2 +2ab+b^2\] \[\huge\rm (ab)^2 = a^2 2ab+b^2\]

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Oh goodness, I came at this a couple of different ways. At first I tried to replace sin and cos theta with regular numbers to see if the setup of the problem was some sort of rule, and that didn't come out right.

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1alright so let sin theta = a cos theta = b so \[\huge\rm (ab)^2 =???\]

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1a^2  b^2?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1\(\color{blue}{\text{Originally Posted by}}\) @Nnesha remember these two formulas \[\huge\rm (a+b)^2 = a^2 +2ab+b^2\] \[\huge\rm (ab)^2 = a^2 2ab+b^2\] \(\color{blue}{\text{End of Quote}}\)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1square of first number and square of 2nd term thne MULTIPLY BOTH TERMS by 2

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1or in other words (ab)^2 is same as (ab)(ab) so you can foil :)

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Okay, I can at least do that...

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1let me know what you get :)

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1\[(\sin \theta  \cos \theta) (\sin \theta  \cos \theta) + (\sin \theta + \cos \theta) (\sin \theta + \cos \theta)\]

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Well, that's at least the first step... am I wrong or doesn't that look like it should cancel out? @Nnesha

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1yes that's right now apply foil method :)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1no no you can't cancel anything yet

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1let sin = x cos = y it will be easy like simple algebra :) (xy)(xy ) :)

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Oh phoey... well I'll continue to solve. If you don't mind, I like to simplify by grouping. (xy)(xy)+(x+y)(x+y) x^2  xy (y) (xy) + (x+y)(x+y) x^2  xy  yx + y^2 + (x+ y) (x+y) x^2  xy  yx + y^2 + x^2 + xy (y)(x+y) x^2  xy  yx + y^2 + x^2 + xy + yx + y^2 x^4 + y^2

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1alright good job thanks! now x^2 +y^2 +x^2 +y^2 here COMBINE LIKE terms when you MULTIPLY same bases THEN you should add their exponent

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge\rm x^2+y^2+x^2+y^2= ??\] combine like terms

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Did I not already do that?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1nope last step is wrong don't add their exponent here is a different COMBINE like terms : x+x = 2x Multiply x times x= x^2 there is a plus sign so you can't add their exponents

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Goodness... I need to fresh up on my basic algebra >.<

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1alright so combine like terms meaning add coefficient of same bases

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1So 2x^4 + 2y^4..?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1yeah but exponent should the same remember exponent rule \[\large\rm x \times x = x^2\] when u MULTIPLY same bases then u should add exponents

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Oh wait it would just be 2x^2 + 2y^2 wouldn't it?

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1That loaded too late^

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1So that leaves me with \[\sin \theta ^{2} + \cos \theta ^{2}\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1now 2 is common factor s take it out \[\huge\rm 2x^2+2y^2\]\[\large\rm 2(x^2+y^2)\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1yes right change back to sin and cos so remember special identity sin^2 x + cos^2 x = what ?

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Ooof... forgot about that!

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1I honestly don't remember.

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1hmm that's the only you shouldn't forget \[\huge\rm sin^2 \theta + \cos^2 \theta =1\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1so replace sin^2 + cos ^2 by 1 :)

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1So it's just 2*1 = 2?

chaotic_butterflies
 one year ago
Best ResponseYou've already chosen the best response.1Yay! Thank you for being so detailed, it really helped

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1my pleasure :) gO_od job!! :=)
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