Question

The coefficient of x in the expansion of sin x/2 + cos x/2 is ​

Answer 1

Answer:

1 is the coefficient of x

Answer 2

The coefficient of x in sin x/2 + cos x/2 is 1/2.

Step-by-step explanation:

Given,

sin x/2 + cos x/2

Find

The coefficient of x in expansion.

So, by expansion formulas we can get,

sin x/2 = $\frac{x}{2} - \frac{(\frac{x}{2}) ^{3} }{3!} + \frac{(\frac{x}{2}) ^{5} }{5!} - \frac{(\frac{x}{2}) ^{7} }{7!} + ...$

cos x/2 = $1 - \frac{(\frac{x}{2}) ^{2} }{2!} + \frac{(\frac{x}{2}) ^{4} }{4!} - \frac{(\frac{x}{2}) ^{6} }{6!}+...$

If we add sin x/2 + cos x/2 =

$[\frac{x}{2} - \frac{(\frac{x}{2}) ^{3} }{3!} + \frac{(\frac{x}{2}) ^{5} }{5!} - \frac{(\frac{x}{2}) ^{7} }{7!} + ...] + [1 - \frac{(\frac{x}{2}) ^{2} }{2!} + \frac{(\frac{x}{2}) ^{4} }{4!} - \frac{(\frac{x}{2}) ^{6} }{6!}+...]$

Here we get 1/2 as coefficient of x.

Therefore the coefficient of x in sin x/2 + cos x/2 = 1/2.