What is the value of cos(75)cos(15)-sin(75)sin(15) ?

The value of cos(75)cos(15)-sin(75)sin(15) is 0

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cos(75)cos(15)-sin(75)sin(15)

cos (7 5^{\circ}) cos (1 5^{\circ}) - sin (7 5^{\circ}) sin (1 5^{\circ})

0

Solution steps

cos (7 5^{\circ}) cos (1 5^{\circ}) - sin (7 5^{\circ}) sin (1 5^{\circ})

Rewrite using trig identities:

cos (9 0^{\circ})

cos (1 5^{\circ}) cos (7 5^{\circ}) - sin (1 5^{\circ}) sin (7 5^{\circ})

Use the Angle Sum identity:

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

= cos (1 5^{\circ} + 7 5^{\circ})

Simplify

= cos (9 0^{\circ})

= cos (9 0^{\circ})

Use the following trivial identity:

cos (9 0^{\circ}) = 0

cos (9 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0

\frac{22}{tan ( 1 2 ^{\circ} )}

cos (arctan (- \frac{2}{3}))

sin (3 0^{\circ}) \cdot 5

3 cos (\frac{5 π}{4})

\frac{2 tan ( \frac{π}{10} )}{1 - tan ^{2} ( \frac{π}{10} )}

What is the value of cos(75)cos(15)-sin(75)sin(15) ?
The value of cos(75)cos(15)-sin(75)sin(15) is 0