Verify the Given Identity $$\frac { \sin u + \sin v } { \cos u + \cos v } = \tan \frac { 1 } { 2 } ( u + v )$$

question 23

Essay

Verify the given identity.
$$\frac { \sin u + \sin v } { \cos u + \cos v } = \tan \frac { 1 } { 2 } ( u + v )$$

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Definitions:

Specializing Exclusively

Involves focusing production or economic activities on a single area or product to maximize efficiency and expertise.

Recession

A momentary economic deflationary period, seen in reduced levels of trade and manufacturing, commonly characterized by a GDP drop for two sequential quarters.

Efficiently

Achieving maximum productivity with minimum wasted effort or expense, often related to the optimal use of resources.

Economic Growth

An increase in the production of economic goods and services, compared from one period of time to another. It can be measured in nominal or real terms, the latter of which is adjusted for inflation.