Question

If θ = 30° verify `tan 2 theta = (2 tan theta)/(1 - tan^2 theta)`

Answer 1

Given θ = 30° ....(1)

To verify

`tan 2 theta = (2 tan theta)/(1 - tan^2 theta)`

Now consider LHS of the expression to be verified in equation (2)

Therefore

L.H.S = `tan 2 theta`

Now by substituting the value of θ from equation (1) in the above expression.

We get

LHS = `tan 2 xx (30^@)`

`= tan 60^@`

`= sqrt3`

Now by substituting the value of θ from equation (1) in the expression `(2 tan theta)/(1- tan^ theta)`

We get

RHS = `(2tan (30^@))/(1 - tan^2 (30^@))`  .....(4)

RHS = `(2xx1/sqrt3)/(1- (1/sqrt3)^2)`

`= (2/sqrt3)/((3-1)/3)`

`= sqrt3`

Now by comparing equation (3) and (4)

We get

LHS = RHS = `sqrt3`

Hence  `tan 2 theta = (2 tan theta)/(1 - tan^2 theta)`