What is the value of cos(45)(sec(45)-cos(45)) ?

The value of cos(45)(sec(45)-cos(45)) is 1/2

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cos(45)(sec(45)-cos(45))

cos (4 5^{\circ}) (sec (4 5^{\circ}) - cos (4 5^{\circ}))

\frac{1}{2}

Solution steps

cos (4 5^{\circ}) (sec (4 5^{\circ}) - cos (4 5^{\circ}))

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

sec (4 5^{\circ}) = 2

= \frac{2}{2} (2 - \frac{2}{2})

Simplify

\frac{2}{2} (2 - \frac{2}{2}) : \frac{1}{2}

= \frac{1}{2}

cos (12 0^{\circ}) cos (4 5^{\circ}) - sin (12 0^{\circ}) sin (4 5^{\circ})

4 sin (\frac{π}{4}) cos (\frac{π}{4})

500 sin (3 5^{\circ})

sec (25 5^{\circ})

arcsec (5 + 3)

What is the value of cos(45)(sec(45)-cos(45)) ?
The value of cos(45)(sec(45)-cos(45)) is 1/2