Question

If tanθ +1/tanθ=2,then show that tan²θ +1/tan²θ= 2 ,Prove it

Answer 1

Let
$\tan( \theta) = x$
Then, We have
$x + \frac{1}{x} = 2$
Squaring both sides,
${(x + \frac{1}{x} )}^{2} = {2}^{2} \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 4 \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 4 \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 4 - 2 = 2$

Hence, we proved
${tan}^{2} ( \theta) + \frac{1}{ {tan}^{2} ( \theta)} = 2$
when
$\tan( \theta) + \frac{1}{ \tan( \theta) } = 2$

Answer 2

In the attachment I have answered this problem.

We use the following algebraic

identity to expand the given

expression .

(a+b) ^2 = a^2 + b^2 + 2ab

See the attachment for detailed solution.