Question

In a right angled triangle ABC, right angle is at B. Ir tan A=root 3, then find the value of
(1) sin A cos C + cos A sin C
(ii) cos A cos C - sin A sin C​

Answer 1

Step-by-step explanation:

In △ABC,

∠B=90

o

, tanA= 1÷√3= AB/BC

Let BC =1x,AB= 3 xAC 2 =AB 2 +BC 2AC 2 =( 3 x) 2 +(x) 2=4x 2

AC=2x

(i) sinAcosC+cosAsinC= 21 × 21 + 23 × 23 = 41 + 43=1

(ii) cosAcosC−sinAsinC= 23 × 21 − 21 × 23 = 43 − 43=0