Differentiate between a conditional equation and an identity?

Complete the sum or difference identity.

$\sin (x+y)=$ __________

Verify the identity.

$${ }_n C_n=1$$

Verify the given identity.

arcsin (-x) = -arcsin x

Prove the given trigonometric identity.

$$\sin (A+B)$$

Determine whether the given equation is an identity. If the equation is not an identity, find all its solutions.

$$e ^ { \sin ^ { 2 } x } e ^ { \cos ^ { 2 } x } = e$$

Is $\tan x=\frac{(\sec x)}{(\csc x)}$ an identity?

Prove the identity.

$$\cosh x-\sinh x=e^{-x}$$

Verify the identity. $\sin$ x $\csc$(-x) = -1

Verify the identity.

$$\arccos (-x) = \pi-\arccos x$$

Verify the identity,.

$$\arccos (-x)=\pi-\arccos x$$

Verify each identity. Give the domain of validity for each identity. $\sin \theta \tan \theta=\frac{1}{\cos \theta}-\cos \theta$

Prove the identity.

$$\cosh x+\sinh x=e^x$$

Verify the identity in (23) by termwise differentiation.