Question

In a ∆ABC, right angled at A, if $\tan \mathrm{C}=\sqrt{3}$, find the value of sin B cos C + cos B sin C.

Answer 1

Given:

To find:

The givenis as shown in figure below

Side BC is unknown and can be found using Pythagoras theorem

Therefore,

Now by substituting the value of known sides from figure (a)

We get,

Now by taking square root on both sides

We get,

Therefore Hypotenuse side BC = 2 …… (1)

Now

Therefore,

Now by substituting the values from equation (1) and figure (a)

We get,

…… (2)

Now

Therefore,

Now by substituting the values from equation (1) and figure (a)

We get,

…… (3)

Now

Therefore,

Now by substituting the values from equation (1) and figure (a)

We get,

…… (4)

Now by definition,

Therefore,

Now by substituting the value of and from equation (4) and given data respectively

We get,

Now gets cancelled as it is present in both numerator and denominator

Therefore,

…… (5)

Now by substituting the value of and from equation (2) , (3) , (4) and (5) respectively in

We get,