If tan α = x +1, tan β = x − 1,

Question:

If tan α = x +1, tan β = x − 1, show that 2 cot (α − β) = x2.

Solution:

$\mathrm{LHS}=2 \cot (\alpha-\beta)$

$=\frac{2(1+\tan \alpha \tan \beta)}{[\tan \alpha-\tan \beta]}$

$=\frac{2+2(x+1)(x-1)}{(x+1-x+1)}$

$=\frac{2+2 x^{2}-2}{2}$

$=\frac{2 x^{2}}{2}$

$=x^{2}$

= RHS

Hence proved.

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now