# 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

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by NakiSarraf

2015-06-10T15:33:24+05:30

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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

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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