Q. 353.8( 20 Votes )

In a ΔABC, right angled at A, if tan C = √3, find the value of sin B cos C + cos B sin C.

Answer :

In a ΔABC, right angled at A,

tan C = √3

i.e ∠C = 60° and ∠B = 90 - 60 = 30°

Sin C = Sin 60° = √3/2

Cos C = Cos 60° = 1/2

Sin B = Sin 30° = 1/2

Cos B = Cos 30° = √3/2 

According to the question,

sin B cos C + cos B sin C

= (1/2) (1/2) + (√3/2) (√3/2)

= 1/4 + 3/4

= 1

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