Question

$\huge\green\tt\frac{ \sqrt{tanx} }{sinxcosx}$
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Answer 1

Question :

$\huge\green\tt\frac{ \sqrt{tan \: x} }{sin \: x \: cos \: x}$

Solution :

$\green\tt\frac{ \sqrt{tan \: x} }{sin \: x \: cos \: x}$

$⇛\green\tt\frac{ \sqrt{tan \: x} }{sin \: x \: cos \: x. \frac{cos \: x}{cos \: x} }$

$⇛\green\tt\frac{ \sqrt{tan \: x} }{sin \: x. \frac{cos ^{2} \: x}{cos \: } }$

$⇛\green\tt\frac{ \sqrt{tan \: x} }{cos ^{2} \: x \: \frac{sin \: x}{cos \: x} }$

$⇛\green\tt\frac{ \sqrt{tanx} }{cos ^{2} \: x. \: tan \: x}$

$⇛(tan \: x) \frac{1}{2 } - 1 \times \frac{1}{ {cos}^{2} \: x }$

$⇛(tan \: x) \frac{ - 1}{2 } \times \frac{1}{ {cos}^{2} \: x }$

$⇛(tan \: x) \frac{ - 1}{2 } \times { {sec}^{2} \: x }$

$⛬ \sqrt \frac{tan \: x}{sin \: x \: cos \: x} = (tan \: x) \frac{ - 1}{2 \: } \times {sec}^{2} x$