What is the value of cos(pi/(16))cos((3pi)/(16))-sin(pi/(16))sin((3pi)/(16)) ?

The value of cos(pi/(16))cos((3pi)/(16))-sin(pi/(16))sin((3pi)/(16)) is (sqrt(2))/2

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cos(pi/(16))cos((3pi)/(16))-sin(pi/(16))sin((3pi)/(16))

cos (\frac{π}{16}) cos (\frac{3 π}{16}) - sin (\frac{π}{16}) sin (\frac{3 π}{16})

\frac{2}{2}

Solution steps

cos (\frac{π}{16}) cos (\frac{3 π}{16}) - sin (\frac{π}{16}) sin (\frac{3 π}{16})

Rewrite using trig identities:

cos (\frac{π}{4})

= cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

= \frac{2}{2}

arctan (\frac{6}{4})

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

sin (1 6^{\circ})

sin (1 7^{\circ})

sin (arctan (3))

What is the value of cos(pi/(16))cos((3pi)/(16))-sin(pi/(16))sin((3pi)/(16)) ?
The value of cos(pi/(16))cos((3pi)/(16))-sin(pi/(16))sin((3pi)/(16)) is (sqrt(2))/2