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Solution assignment 01 Addition and subtraction formulas
Solution assignment 02 Addition and subtraction formulas
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Solution assignment 06 Addition and subtraction formulas
Solution assignment 07 Addition and subtraction formulas
Solution assignment 08 Addition and subtraction formulas
Solution assignment 09 Addition and subtraction formulas
Solution assignment 10 Addition and subtraction formulas

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Solution assignment 10 Addition and subtraction formulas

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Assignment 10

Show:

$\cos(x+\displaystyle\frac{\pi}{2})=-\sin(x)$

Solution

We rewrite the left-hand side:

$\cos(x+\displaystyle\frac{\pi}{2})=\cos(x)\cos(\displaystyle\frac{\pi}{2})-\sin(x)\sin(\displaystyle\frac{\pi}{2})=$

$\cos(x).0-\sin(x).1=-\sin(x)$

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