(Q19)In a right angled triangle ABC,right angle is at B.if tan A=√3 then find the value of

(i) sin A cos C+ cos A sin C (ii) cos A cos C-sinA sin C

Solution:

ABC1k√3k
Given,tan A=
√3
1
Hence ,
opposite side
adjacent side
 =
√3
1

Let opposite side =√3k and adjacent side=1k

In right angled triangle ABC,

AC2=AB2+BC2

(By pythagoras theroem)

AC2=k2

AC=k

Now,

sin A=
BC
AC
=
√

cos A=
AB
AC
=

sin C=
AB
AC
=

cos C=
BC
AC
=
√

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

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