Identity transformations of Trigonometric Expressions.
prove the following identities.
$\frac{\sqrt{2}}{2} (c o s α + s i n α) = c o s (\frac{π}{4} - α) .$

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Solution

$\frac{\sqrt{2}}{2} (c o s α + s i n α) = c o s (π / 4 - α)$
$= \frac{1}{\sqrt{2}} (c o s α + s i n α)$
$= \frac{1}{\sqrt{2}} c o s α + \frac{1}{\sqrt{2}} s i n α$
$= c o s π / 4 c o s α + s i n π / 4 s i n α$
$= c o s (π / 4 - α) = R . H . S .$
Hence proved

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