What is the value of cos(100)cos(40)+sin(100)sin(40) ?

The value of cos(100)cos(40)+sin(100)sin(40) is 1/2

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cos(100)cos(40)+sin(100)sin(40)

cos (10 0^{\circ}) cos (4 0^{\circ}) + sin (10 0^{\circ}) sin (4 0^{\circ})

\frac{1}{2}

Solution steps

cos (10 0^{\circ}) cos (4 0^{\circ}) + sin (10 0^{\circ}) sin (4 0^{\circ})

Rewrite using trig identities:

cos (6 0^{\circ})

= cos (6 0^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

= \frac{1}{2}

tan^{2} (1 5^{\circ})

\frac{100}{cos ( 3 0 ^{\circ} )}

1 - cos (\frac{3 π}{4})

sin (21 7^{\circ})

\frac{sin ( 12 0 ^{\circ} )}{tan ( 4 5 ^{\circ} ) + sin ( 21 0 ^{\circ} ) cos ( 30 0 ^{\circ} )}

What is the value of cos(100)cos(40)+sin(100)sin(40) ?
The value of cos(100)cos(40)+sin(100)sin(40) is 1/2