Let S=x-(x^(3))/(3!)+(x^(5))/(5!)… and C...

Let `S=x-(x^(3))/(3!)+(x^(5))/(5!)`… and `C=1-(x^(2))/(2!)+(x^(4))/(4!)` Then,

`C^(2)+S^(2)` is not independent of x

2CS = sin 2x

`C^(2)-S^(2)` is independent of x

none of these

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Verified by Experts

The correct Answer is:

a,b,c

We have
`C+is =(1-(x^(2))/(2!)+(x^(4))/(4!)+…)+i(x-(x^(3))/(3!)+(x^(5))/(5!)..)`
`rarr C+is =e^(ix)=cos x +I sin x`
`therefore C= cos x and s= sin x`
`rarr 2CS = sin 2x , C^(2)+S^(2)=1 and C^(2)-S^(2)=cos 2x`

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