Question

if tan a+1/tan a=2,find the value of tan^2a+1/tan^2a​

Answer 1

Answer:

$\large{\underline{\boxed{\sf tan^2 (a) + \dfrac{1}{tan^2 (a)} = 2}}}$

Step-by-step explanation:

Given that ;

$\rm tan(a) + \dfrac{1}{ \tan(a) } = 2$

On squaring both sides,

$\left[ \tan(a) + \frac{1}{ \tan(a) } \right]^{2} = (2)^{2} \\ \\\tan ^{2} (a) + \frac{1}{ \tan {}^{2}(a)} + 2 . \tan(a) . \ \frac{1}{ \tan(a) } = 4 \\ \\ \tan ^{2} (a) + \frac{1}{ \tan {}^{2}(a)} + 2 = 4 \\ \\ \tan ^{2} (a) + \frac{1}{ \tan {}^{2}(a)} = 4 - 2 \\ \\ \boxed{ \red{ \tan ^{2} (a) + \frac{1}{ \tan {}^{2}(a)} = 2}}$

Hence, the answer is 2.

Answer 2

Refer the attachment.