Prove the Identity $$\sin \left( \frac { \pi } { 4 } + x \right) = 2 \sqrt { 2 } ( \cos x + \sin x )$$

question 187

Essay

Prove the identity.
- $$\sin \left( \frac { \pi } { 4 } + x \right) = 2 \sqrt { 2 } ( \cos x + \sin x )$$

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Definitions:

Somatic Nervous System

A part of the peripheral nervous system responsible for voluntary movements of muscles and the reception of external stimuli.

Autonomic Nervous System

The part of the nervous system that controls involuntary bodily functions, including heart rate, digestion, and respiratory rate, consisting of the sympathetic and parasympathetic divisions.

Somatic Nervous System

Part of the peripheral nervous system that handles voluntary control of body movements through the control of skeletal muscles, and also mediates sensory information.

Peripheral Nervous

Part of the nervous system that consists of the nerves and ganglia outside of the brain and spinal cord, responsible for connecting the CNS to limbs and organs.