Trig Identities (Sum and double Angle)

Hi guys, i have a couple question from my homework i am having trouble with a little more then a couple :(, if any one could help i would appreciate it.

1) Simplify or combine where possible, sin(x + x) = i get 2sinx (Answer is sin2x) why is the 2 there? not in front?

2) 5sinxsinx = i get 5sinx^2 (answer is 5sin^2x)

Thanks in advance.

Re: Trig Identities (Sum and double Angle)

Surely you understand that x + x = 2x...

As for the second, if you meant [tex]\displaystyle 5\left[ \sin{(x)} \right] ^2 [/math], this is an equivalent way of writing $\displaystyle \displaystyle 5\sin^2{(x)} $ so you would be correct. However, if you meant $\displaystyle \displaystyle 5\sin{ \left( x^2 \right) }$ you would be wrong.

Re: Trig Identities (Sum and double Angle)

1+1 = 2 O.O who would of guessed yeah i get that lol.

For the second one it is not showing your text correctly. My answer is 5sinx(sinx)= 5

Thanks for the help.

Re: Trig Identities (Sum and double Angle)

What? You think that sinx(sinx)= 1? For **any** a, a times a is designated "$\displaystyle a^2$". That's what that "$\displaystyle ^2$" **means**. So in particular, $\displaystyle (sin x)(sin x)= (sin x)^2$ and $\displaystyle sin^2 x$ is just simpler notation. Strictly speaking "x" is an argument of the **function** "sin" so we should have parentheses. Perhaps if it were (sin(x))(sin(x)) it would be clearer that it should be sin^2(x), not "$\displaystyle sin x^2$" which would be interpreted as "$\displaystyle sin(x^2)$".

Re: Trig Identities (Sum and double Angle)

After reading your comments i understand what i was not getting sometimes its the simple things that get me, One last follow up question if you math wizards don't mind,

Prove the following Cos(x-Pi)=Sin(x+3pi/2) : What i attempted to do was use the identity Sin(a+b)= sinAcosB+cosAsinB it came close but not what i needed, would any one be able to help?.

Thanks for all the help again i really do love this site, and sorry for my stupid questions :(.

Re: Trig Identities (Sum and double Angle)

Expand both sides of the equation using the cosine and sine angle addition identity, respectively.

Re: Trig Identities (Sum and double Angle)