Question

the expression cos80° cos70°+ sin80° sin 70° is equivalent to ​

Answer 1

cos80cos70+sin80sin70

= cosAcosB+sinAsinB, where A=80 and B=70

Thus, it is equivalent to cos(A-B)

cos(80-70)= cos10

Answer 2

Given :

$\cos80^\circ \cos70^\circ+ \sin80^\circ \sin 70^\circ$

To find : the equivalent expression = ?

Solution :

As we know that

$\cos A\cos B+\sin A\sin B=cos(A-B)$

Here,

$A=80^\circ\\\\B=70^\circ$

So, using the formula we get :

$\cos(80^\circ-70^\circ)=\cos10^\circ$

Hence, the equivalent expression is $\cos 10^\circ$