Question

In triangle ABC, right-angled at B, if tan A = 1/route 3
find the value of:
(1) sin A cos C + cos A sin C
(i) cos A cos C - sin A sin C
​

Answer 1

Angle A=30degree

angle B=90 degree

then angle C=60 degree

sinA cosC+cosA sinC=sin(A+C)=sin(30+60)=sin90=1

And

cosA cos C - sinA sin C= cos(a+c)= cos (30+60)=0

Answer 2

In right angled triangle ABC,

tanA= 1/root3

tan A will be equal to 1/root3 only when A=30 degrees

And by angle sum property in triangle ABC, we get C=60 degrees

(i) sinAcosC+cosAsinC

=> 1/2* 1/2+root3/2*root3/2

=> 1/4+3/4= 4/4

=> 1....

(ii) cosAcosC-sinAsinC

=> root3/2*1/2-1/2*root3/2

=> 0....