Question

kindly help me with question number 23.​

Answer 1

Question :

If $\sf{tan\alpha+cot\alpha=2}$ then $\sf{\sqrt{tan\alpha}+\sqrt{cot\alpha}}$=?

1. $\sf{\sqrt{2}}$
2. $\sf{2\sqrt{2}}$
3. 2
4. $\sf{4\sqrt{2}}$

Solution :

$\sf{tan\alpha+cot\alpha=2}$

$\to\sf{tan\alpha+\dfrac{1}{tan\alpha}=2}$

$\to\sf{\dfrac{tan^2\alpha+1}{tan\alpha}=2}$

$\to\sf{tan^2\alpha+1=2tan\alpha}$

$\to\sf{tan^2\alpha-2tan\alpha+1=0}$

$\to\sf{(tan\alpha-1)^2=0}$

$\to\sf{(tan\alpha-1)=0}$

$\to\sf{tan\alpha=1}$

We know ,

${\boxed{\sf{cot\alpha=\dfrac{1}{tan\alpha}}}}$

Then,

$\to\sf{cot\alpha=\dfrac{1}{1}=1}$

$\sf{Now\:find\:the\: value\:of\:\sqrt{tan\alpha}+\sqrt{cot\alpha}}$.

$\sf{\sqrt{tan\alpha}+\sqrt{cot\alpha}}$

• Put $\sf{tan\alpha=1\:and\:cot\alpha=1}$

$\to\sf{\sqrt{1}+\sqrt{1}}$

$\to\sf{1+1}$

$\to\sf{2\:[Answer]}$

Therefore , Option (3) 2 is the correct answer.

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More information :-

• Some trigonometric formulas :-

★ sin²A + cos²A = 1

★ 1 + tan²A = sec²A

★ 1 + cot²A = cosec²A

★ cos²A - sin²A = cos2A