What is the value of cos(70)cos(25)+sin(70)sin(25) ?

The value of cos(70)cos(25)+sin(70)sin(25) is (sqrt(2))/2

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cos(70)cos(25)+sin(70)sin(25)

cos (7 0^{\circ}) cos (2 5^{\circ}) + sin (7 0^{\circ}) sin (2 5^{\circ})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

cos (7 0^{\circ}) cos (2 5^{\circ}) + sin (7 0^{\circ}) sin (2 5^{\circ})

Rewrite using trig identities:

cos (4 5^{\circ})

cos (7 0^{\circ}) cos (2 5^{\circ}) + sin (7 0^{\circ}) sin (2 5^{\circ})

Use the Angle Difference identity:

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

= cos (7 0^{\circ} - 2 5^{\circ})

Simplify

= cos (4 5^{\circ})

= cos (4 5^{\circ})

Use the following trivial identity:

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

cos (4 5^{\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}

= \frac{2}{2}

= \frac{2}{2}

sin (2) (90)

\frac{π}{6} sin (\frac{π}{6})

arctan (\frac{7}{- 5})

10 cos (13 5^{\circ})

- 29 \cdot cos (4 5^{\circ})

What is the value of cos(70)cos(25)+sin(70)sin(25) ?
The value of cos(70)cos(25)+sin(70)sin(25) is (sqrt(2))/2