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

question 19

Essay

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

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Definitions:

Pension Expense

The cost recognized by an employer for maintaining a defined benefit pension plan for its employees over a specific period.

Plan Assets

Assets that are held within a pension or retirement plan for the purpose of funding participant benefits.

Actuarial Loss

A loss recognized when the actual experience under a pension plan deviates from expected assumptions, resulting in increased liabilities or decreased assets.

Unrecognized Actuarial (Gain)Loss

Financial gains or losses in pension plans or other post-employment benefit plans that have not been recognized in financial statements.