Question

Find the value of x in the following:

`sqrt3 sin x = cos x`

Answer 1

We have

`sqrt3 sin x = cos x`

Now by cross multiplying we get,

`sqrt3 sin x = cos x``

`=> sin x/cos x = 1/sqrt3`.........(1)

Now we know that

`sin x/cos x = tan x` .......(2)

Therefore from equation (1) and (2)

We get

`tan x = 1/sqrt3` .......(3)

since

`tan 30^2 = 1/sqrt3` ....(4)

Therefore, by comparing equation (3) and (4) we get,

`x = 30^@`

Therefore

`x = 30^@`