Question

sin^2 (x/2 )+cos^2(x/2)=? integration ​

Answer 1

Answer:

1

Step-by-step explanation:

Use sin (t)² + cos (t)² = 1 to simplify the expression.

$\sin( \frac{x}{2} )^{2} + \cos( \frac{x}{2} )^{2} \\ = 1$

Answer 2

Given:

sin^2 (x/2 )+cos^2(x/2)

To Find:

To find the integration wrt x

Solution:

To Find the integration with respect to x, we will express the equation as,

$\int{[sin^2(\frac{x}{2})+cos^2(\frac{x}{2} )] } \, dx$

the following integration is definite integration as nothing about the limiting values has been mentioned, and also we should know that the trigonometric identity,

cos^2x + sin^2x=1

And in the given integration same will be applied which will make the whole integration with constant '1', which goes as,

$=\int{[sin^2(\frac{x}{2})+cos^2(\frac{x}{2} )] } \, dx \\=\int{1} \, dx$

and we should also know that the integration of a constant wrt x is x itself, therefore the expression can be now written as,

$=\int{1} \, dx \\=x+C$

where C is a constant.

Hence, the integration of sin^2 (x/2 )+cos^2(x/2) is (x+C).