Question

In triangle ABC right angled at B, if tan A=
/√

, find the value of

(i) Sin A Cos C + cos A Sin C
(ii) Cos A Cos C - sin A Sin C​

Answer 1

Answer:

Here, we are given,

tanA=13‾√=tan30∘

So, A=30∘

As, B=90∘,C=180−90−30=60∘

(i)sinAcosC+cosAsinC

We know, sin(x+y)=sinxcosy+cosxsiny

∴sinAcosC+cosAsinC=sin(A+C)=sin(30+60)=sin90∘=1

(ii)cosAcosC−sinAsinC

We know, cos(x+y)=cosxcosy−cosxcosy

∴cosAcosC−sinAsinC=cos(A+C)=cos(30+60)=cos90∘=0