Question

Tan alpha +cot alpha =2 then root tan alpha + root cot alpha =?

Answer 1

$\textbf{Given:}$

$tan\alpha+cot\alpha =2$

$\textbf{To find:}$

$\text{The value of \sqrt{tan\alpha}+\sqrt{cot\alpha} }$

$\textbf{Solution:}$

$\text{Consider,}$

$(\sqrt{tan\alpha}+\sqrt{cot\alpha})^2$

$\text{Using the algebraic identity,}$

$\boxed{\bf(a+b)^2=a^2+b^2+2\,ab}$

$=(\sqrt{tan\alpha})^2+(\sqrt{cot\alpha})^2+2\,\sqrt{tan\alpha}\,\sqrt{cot\alpha}$

$=tan\alpha+cot\alpha+2\,\sqrt{tan\alpha}(\dfrac{1}{\sqrt{tan\alpha}})$

$=2+2(1)$

$=2+2$

$=4$

$\implies\,(\sqrt{tan\alpha}+\sqrt{cot\alpha})^2=4$

$\text{Taking square root on bothsides, we get}$

$\bf\,\sqrt{tan\alpha}+\sqrt{cot\alpha}=2$

$\textbf{Answer:}$

$\textbf{The value of \bf\sqrt{tan\alpha}+\sqrt{cot\alpha} is 2}$

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Answer 2

Answer:

answer is 2

Step-by-step explanation:

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