Question

simply cos100°.cos40°+sin100°.sin40°​

Answer 1

Answer:

1/2

Step-by-step explanation:

cos100 cos40 + sin100 sin40

it's in the form of cos(A-B) =cosAcosB+sinAsinB

then it is cos(100-40)

that's cos60

cos60=1/2

therefore cos100 cos40 + sin100 sin40=1/2

Answer 2

$\cos(100) . \cos(40) + \sin(100) . \sin(40 )$

$\tt We \: know \: that,$

$\blue{ \boxed{\cos( \alpha ) \cos( \beta ) + \sin( \alpha ) \sin( \beta ) = \cos( \alpha - \beta ) }}$

$\implies \cos(100 - 40)$

$\implies \cos(60)$

$\orange{ \therefore\cos(100) . \cos(40) + \sin(100) . \sin(40 ) = \frac{1}{2} }$