Question

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

Answer 1

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

Answer 2

sinBcosC+coBsinC

=sin(B+C)

=sin (180-A)

=sin A

=sin 90

=1