Question

- Prove that 1+sin(x)- Cos(x)= 2 Sin(1/2x) [ Cos(1/2x) +Sin(1/2x) ]

I'm stuck at the last step for like an hour or so
reached this
1+sin(x)- Cos(x) = Sin(X) + 2Sin^2(1/2x)

Help please :)

Answer 1

Welcome to OpenStudy :D
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Answer 2

Remember \(1−\cos(2x)\)?

Answer 3

No ++"

Answer 4

& yeah sure :) for the medal thing ^^

Answer 5

lol that's just my welcome msg for new ppl like u

Answer 6

ok if you look into that step, you'll find that \(\sin(x)\) exists in both sides

Answer 7

yeah , the 1+sin(x)- Cos(x) = Sin(X) + 2Sin^2(1/2x) , right ?

Answer 8

so you just have to prove that \(1-\cos(x)=2\sin^2\left(\dfrac12x\right)\)

Answer 9

I did it !
\[1- cosx = 2\sin ^{2 \left(\begin{matrix}1 \\ 2\end{matrix}\right)} x \]
which is equal to
\[1-\left( 1-2\sin ^{2\left(\begin{matrix}1 \\ 2\end{matrix}\right)} \right)x = 2\sin ^{2\left(\begin{matrix}1 \\ 1\end{matrix}\right)}x \] :D
Thanks so much ! really appreciate it and for the welcome message too :D

Answer 10

you can use \frac12 for \(\frac12\) :)

Answer 11

and no problem :)

Answer 12

yeah just noticed it :) Thanks for your help ^^