What is the value of cos(310)cos(50)-sin(310)sin(50) ?

The value of cos(310)cos(50)-sin(310)sin(50) is 1

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cos(310)cos(50)-sin(310)sin(50)

cos (31 0^{\circ}) cos (5 0^{\circ}) - sin (31 0^{\circ}) sin (5 0^{\circ})

1

Solution steps

cos (31 0^{\circ}) cos (5 0^{\circ}) - sin (31 0^{\circ}) sin (5 0^{\circ})

Rewrite using trig identities:

cos (0)

cos (31 0^{\circ}) cos (5 0^{\circ}) - sin (31 0^{\circ}) sin (5 0^{\circ})

Use the Angle Sum identity:

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

= cos (31 0^{\circ} + 5 0^{\circ})

Simplify

= cos (36 0^{\circ})

cos (36 0^{\circ}) = cos (0)

cos (36 0^{\circ})

Rewrite

36 0^{\circ}

36 0^{\circ} + 0

= cos (36 0^{\circ} + 0)

Apply the periodicity of

cos

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 0) = cos (0)

= cos (0)

= cos (0)

= cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

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}

= 1

= 1

arctan (\frac{6}{- 6})

cos (\frac{29 π}{12})

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

tan (arccos (\frac{24}{25}) - arcsin (\frac{12}{13}))

cot (2 9^{\circ})

What is the value of cos(310)cos(50)-sin(310)sin(50) ?
The value of cos(310)cos(50)-sin(310)sin(50) is 1