The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

C2 Trig: proving identities

How dfq does(1-sin^2x)+2sinx equal 2-(sin^2x-2sinx+1)?

It doesn't make any sense at all. Can anyone give me a method I could use? thx :d
Original post by CookieHero
How dfq does(1-sin^2x)+2sinx equal 2-(sin^2x-2sinx+1)?

It doesn't make any sense at all. Can anyone give me a method I could use? thx :d


2-(sin^2x-2sinx+1) = 2 - sin^2x + 2 sinx - 1 = 1 - sin^2x + 2 sin x, as required.
Reply 2
Avatar for joostan
joostan
13
Original post by CookieHero
How dfq does(1-sin^2x)+2sinx equal 2-(sin^2x-2sinx+1)?

It doesn't make any sense at all. Can anyone give me a method I could use? thx :d


It's a simple manipulation, they've simply added one, then subtracted it again. So:
(1−sin⁡2(x))+2sin⁡(x)=[1−(sin⁡2(x)−2sin⁡(x))]+1−1=(2−sin⁡2(x)+2sin⁡(x)+1)(1-\sin^2(x))+2\sin(x)=[1-(\sin^2(x)-2\sin(x))]+1-1=(2-\sin^2(x)+2\sin(x)+1).
Original post by joostan
It's a simple manipulation, they've simply added one, then subtracted it again. So:
(1−sin⁡2(x))+2sin⁡(x)=[1−(sin⁡2(x)−2sin⁡(x))]+1−1=(2−sin⁡2(x)+2sin⁡(x)+1)(1-\sin^2(x))+2\sin(x)=[1-(\sin^2(x)-2\sin(x))]+1-1=(2-\sin^2(x)+2\sin(x)+1).


My method of starting from the RHS is far simpler as it doesn't require seeing the "trick" of adding 1 etc.
Original post by ConstatSententia
My method of starting from the RHS is far simpler as it doesn't require seeing the "trick" of adding 1 etc.


He used LaTeX though so his looks way cooler.
Reply 5
Avatar for joostan
joostan
13
Original post by ConstatSententia
My method of starting from the RHS is far simpler as it doesn't require seeing the "trick" of adding 1 etc.


If this is the entirety of the identity I agree, I was however assuming that this is one step in a more complicated identity, in which case manipulating the first expression into the second may be a priority.
Original post by joostan
If this is the entirety of the identity I agree, I was however assuming that this is one step in a more complicated identity, in which case manipulating the first expression into the second may be a priority.


noli sine ratione rem postulare.
Reply 7
Avatar for CookieHero
CookieHero
OP
3
Thanks for your help everyone :biggrin::biggrin:

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you