Question

In triangle ABC, right-angled at B, if tan A = 1/SQRT3 find the value of:
(i) sin A cos C + cos A sin C
(ii) cos A cos C – sin A sin C

NCERT Class X
Mathematics - Mathematics

Chapter _INTRODUCTION TO
TRIGONOMETRY

Answer 1

we know A + B + C = π      => π - B = (A+C)

Sin A Cos C + Cos A  Sin C = Sin (A + C) = Sin (π - B)  = Sin B = sin π/2 = 1
Cos A Cos C - Sin A SIn C = Cos (A + C) = Cos (π - B) = - Cos B = 0

==============================
Tan A  = 1/√3    =>  A = π/6
B = π/2
   =>  C = π - π/6 - π/2 = π/3

A + C = π/3 + π/6 = π/2

Sin A Cos C + Cos A  Sin C = Sin (A + C) = Sin (π/6 + π/3) = Sin π/2 = 1

Cos A Cos C - Sin A Sin C = Cos (A + C) = Cos π/2 = 0