Some Applications Of Trigonometry

Question

In triangle ABC, right angled at B, if $WiredFaculty$ find the value of :
(i) sin A cos C + cos A sin C
(ii) cos A .cos C - sin A.sin C.

Solution

We have,
$WiredFaculty$
Let $WiredFaculty$
Using Pythagoras theorem, we have
$WiredFaculty$
AC = 2K
So,
AC = 2K

$WiredFaculty$
and , $cos space straight C space equals space BC over AC equals fraction numerator straight K over denominator 2 straight K end fraction equals 1 half$
Now,
(i) sin A cos C + cos A sin C
$WiredFaculty$
(ii) cos A. cos C - sin A .sin C
$WiredFaculty$