In triangle ABC, right-angled at B, if find the value of:

(i) Sin A Cos C + Cos A Sin C

(ii) Cos A Cos C – Sin A Sin C

tan A = =

If BC is *k*, then AB will be, where *k* is a positive integer

In ΔABC,

AC^{2} = AB^{2} + BC^{2}

= ()^{2} + (k)^{2}

= 3*k*^{2} + *k*^{2} = 4*k*^{2}

AC = 2*k*

Sin A =

= =

Cos A =

= =

Sin C =

= =

Cos C =

= =

(i) sin A cos C + cos A sin C

= ( () + (

=

=

(ii) cos A cos C - sin A sin C

= () () – () ()

=

= 0

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